US2009213985A1PendingUtilityA1

System and method for tomographic reconstruction utilizing circular trajectory and scanogram to reduce artifacts

Assignee: TOSHIBA KKPriority: Oct 31, 2007Filed: Sep 25, 2008Published: Aug 27, 2009
Est. expiryOct 31, 2027(~1.3 yrs left)· nominal 20-yr term from priority
A61B 6/032A61B 6/027
53
PatentIndex Score
0
Cited by
0
References
0
Claims

Abstract

A computed tomography apparatus and method using line data estimated from circle data and scanogram data. An image of a subject is reconstructed using the circle data and the estimated line data. The circle data and scanogram data may be weighted in estimating the line data. The apparatus and method are useful in diminishing or eliminating streak artifacts in reconstructed images such as images including the spine.

Claims

exact text as granted — not AI-modified
1 . A computed-tomography apparatus, comprising:
 an x-ray source;   an x-ray detector disposed to receive x-rays from said x-ray source;   a unit to collect circle data and scanogram data;   a processing unit for estimating line data from said circle data and said scanogram data and for performing reconstruction of an image using said circle data and said estimated line data.   
   
   
       2 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to estimated said line data using: 
     
       
         
           
             
               
                 P 
                 L 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 
                   v 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     C 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                       , 
                       
                         λ 
                         0 
                       
                     
                     ) 
                   
                 
               
               + 
               
                 
                   h 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     S 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data and P S (u, z) is said scanogram data. 
   
   
       3 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to estimated said line data using: 
     
       
         
           
             
               
                 P 
                 L 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 w 
                                 1 
                               
                                
                               
                                 
                                   P 
                                   C 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                     , 
                                     
                                       λ 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               v 
                             
                             > 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     w 
                                     1 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   P 
                                   S 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             
                               
                                 w 
                                 2 
                               
                                
                               
                                 
                                   P 
                                   C 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           
                                             - 
                                             u 
                                           
                                           , 
                                           
                                             
                                               v 
                                               ′ 
                                             
                                             + 
                                             h 
                                           
                                           , 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             λ 
                                             0 
                                           
                                           + 
                                           π 
                                           - 
                                           
                                             2 
                                              
                                             
                                                 
                                             
                                              
                                             γ 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               v 
                             
                             < 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     w 
                                     2 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   P 
                                   S 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                               
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       w 
                       1 
                     
                   
                   = 
                   
                     
                       
                         v 
                         
                           v 
                           + 
                           h 
                         
                       
                        
                       
                         
 
                       
                        
                       
                         w 
                         2 
                       
                     
                     = 
                     
                       - 
                       
                         
                           2 
                            
                           v 
                            
                           
                               
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           u 
                         
                         h 
                       
                     
                   
                 
                 , 
                 
                   
                     
                       
                         
                           
                             
                               v 
                               ′ 
                             
                             = 
                             
                               v 
                               
                                 
                                   cos 
                                   2 
                                 
                                  
                                 u 
                               
                             
                           
                         
                         
                           
                             for 
                              
                             
                                 
                             
                              
                             a 
                              
                             
                                 
                             
                              
                             cylindrical 
                              
                             
                                 
                             
                              
                             detector 
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       w 
                       2 
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           2 
                            
                           v 
                         
                         h 
                       
                     
                      
                     
                       
                         SDD 
                         2 
                       
                       
                         
                           SDD 
                           2 
                         
                         + 
                         
                           u 
                           2 
                         
                       
                     
                   
                 
                 , 
                 
                   
                     v 
                     ′ 
                   
                   = 
                   
                     v 
                      
                     
                       
                         
                           
                             SDD 
                             2 
                           
                           + 
                           
                             u 
                             2 
                           
                         
                         
                           SDD 
                           2 
                         
                       
                     
                      
                     
                         
                     
                      
                     for 
                      
                     
                         
                     
                      
                     a 
                      
                     
                         
                     
                      
                     flat 
                      
                     
                         
                     
                      
                     detector 
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data, P S (u, z) is said scanogram data, and w 1  and w 2  are weighting factors. 
   
   
       4 . An apparatus as recited in  claim 2 , wherein said processing unit is further configured to estimate said line data using 
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       5 . An apparatus as recited in  claim 3 , wherein said processing unit is further configured to estimate said line data using 
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       6 . An apparatus as recited in  claim 3 , wherein said weighting factors comprise:
     w   1S =3 w   1   2 −2 w   1   3 .       w   2S =3 w   2   2 −2 w   2   3 .   
   
   
       7 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to estimate said line data using multiple scanogram rays for each estimated line ray. 
   
   
       8 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to estimate said line data using one of local smoothing and adaptive filtering. 
   
   
       9 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to reconstruct said image using one of filtered backprojection type reconstruction and backprojection filtration type reconstruction. 
   
   
       10 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to reconstruct said image using full revolution circular data. 
   
   
       11 . An apparatus as recited in  claim 1 , wherein said processing unit is configured to reconstruct said image using partial revolution circular data. 
   
   
       12 . A computed tomography method, comprising:
 exposing a subject to x-rays;   collecting circle data;   collecting scanogram data;   estimating line data using said circle data and said scanogram data; and   reconstructing an image of said subject using said estimated line data and said circle data.   
   
   
       13 . A method as recited in  claim 12 , comprising estimating said line data using: 
     
       
         
           
             
               
                 P 
                 L 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 
                   v 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     C 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                       , 
                       
                         λ 
                         0 
                       
                     
                     ) 
                   
                 
               
               + 
               
                 
                   h 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     S 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data and P S (u, z) is said scanogram data. 
   
   
       14 . A method as recited in  claim 12 , comprising estimating said line data using: 
     
       
         
           
             
               
                 P 
                 L 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 w 
                                 1 
                               
                                
                               
                                 
                                   P 
                                   C 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                     , 
                                     
                                       λ 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               v 
                             
                             > 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     w 
                                     1 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   P 
                                   S 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             
                               
                                 w 
                                 2 
                               
                                
                               
                                 
                                   P 
                                   C 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           
                                             - 
                                             u 
                                           
                                           , 
                                           
                                             
                                               v 
                                               ′ 
                                             
                                             + 
                                             h 
                                           
                                           , 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             λ 
                                             0 
                                           
                                           + 
                                           π 
                                           - 
                                           
                                             2 
                                              
                                             
                                                 
                                             
                                              
                                             γ 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               v 
                             
                             < 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     w 
                                     2 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   P 
                                   S 
                                 
                                  
                                 
                                   ( 
                                   
                                     u 
                                     , 
                                     
                                       v 
                                       + 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                               
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       w 
                       1 
                     
                   
                   = 
                   
                     
                       
                         v 
                         
                           v 
                           + 
                           h 
                         
                       
                        
                       
                         
 
                       
                        
                       
                         w 
                         2 
                       
                     
                     = 
                     
                       - 
                       
                         
                           2 
                            
                           v 
                            
                           
                               
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           u 
                         
                         h 
                       
                     
                   
                 
                 , 
                 
                   
                     
                       
                         
                           
                             
                               v 
                               ′ 
                             
                             = 
                             
                               v 
                               
                                 
                                   cos 
                                   2 
                                 
                                  
                                 u 
                               
                             
                           
                         
                         
                           
                             for 
                              
                             
                                 
                             
                              
                             a 
                              
                             
                                 
                             
                              
                             cylindrical 
                              
                             
                                 
                             
                              
                             detector 
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       w 
                       2 
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           2 
                            
                           v 
                         
                         h 
                       
                     
                      
                     
                       
                         SDD 
                         2 
                       
                       
                         
                           SDD 
                           2 
                         
                         + 
                         
                           u 
                           2 
                         
                       
                     
                   
                 
                 , 
                 
                   
                     v 
                     ′ 
                   
                   = 
                   
                     v 
                      
                     
                       
                         
                           
                             SDD 
                             2 
                           
                           + 
                           
                             u 
                             2 
                           
                         
                         
                           SDD 
                           2 
                         
                       
                     
                      
                     
                         
                     
                      
                     for 
                      
                     
                         
                     
                      
                     a 
                      
                     
                         
                     
                      
                     flat 
                      
                     
                         
                     
                      
                     detector 
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data, P S (u, z) is said scanogram data, w 1  and w 2  are weighting factors. 
   
   
       15 . A method as recited in  claim 12 , comprising estimating said line data using 
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       16 . A method as recited in  claim 14 , comprising estimating said line data using 
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       17 . An method as recited in  claim 14 , wherein said weighting factors comprise
     w   1S =3 w   1   2 −2 w   1   3 .       w   2S =3 w   2   2 −2 w   2   3 .   
   
   
       18 . A method as recited in  claim 12 , comprising estimating said line data using multiple scanogram rays for each estimated line ray. 
   
   
       19 . A method as recited in  claim 12 , comprising estimating said line data using one of local smoothing and adaptive filtering. 
   
   
       20 . A method as recited in  claim 12 , wherein said reconstructing comprises one of filtered backprojection type reconstruction and backprojection filtration type reconstruction. 
   
   
       21 . A method as recited in  claim 12 , wherein said reconstructing comprises reconstruction of full revolution circular data. 
   
   
       22 . A method as recited in  claim 12 , wherein said reconstructing comprises reconstruction of partial revolution circular data. 
   
   
       23 . A computer readable-medium containing instructions that may be executed by a computer to perform a method, comprising:
 collecting circle data from an x-ray scan of a subject;   collecting scanogram data from said x-ray scan;   estimating line data using said circle data and said scanogram data; and   reconstructing an image of said subject using said estimated line data and said circle data.   
   
   
       24 . A medium as recited in  claim 23 , wherein method comprises:
 estimating said line data using:   
     
       
         
           
             
               
                 P 
                 L 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 
                   v 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     C 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                       , 
                       
                         λ 
                         0 
                       
                     
                     ) 
                   
                 
               
               + 
               
                 
                   h 
                   
                     v 
                     + 
                     h 
                   
                 
                  
                 
                   
                     P 
                     S 
                   
                    
                   
                     ( 
                     
                       u 
                       , 
                       
                         v 
                         + 
                         h 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data and P S (u, z) is said scanogram data. 
   
   
       25 . A medium as recited in  claim 23 , wherein said method comprises:
 estimating said line data using:   
     
       
         
           
             
                 
             
              
             
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
               = 
               
                 { 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   w 
                                   1 
                                 
                                  
                                 
                                   
                                     P 
                                     C 
                                   
                                    
                                   
                                     ( 
                                     
                                       u 
                                       , 
                                       
                                         v 
                                         + 
                                         h 
                                       
                                       , 
                                       
                                         λ 
                                         0 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                             
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 v 
                               
                               > 
                               0 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       w 
                                       1 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   
                                     P 
                                     S 
                                   
                                    
                                   
                                     ( 
                                     
                                       u 
                                       , 
                                       
                                         v 
                                         + 
                                         h 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               , 
                             
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   w 
                                   2 
                                 
                                  
                                 
                                   
                                     P 
                                     C 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             
                                               - 
                                               u 
                                             
                                             , 
                                             
                                               
                                                 v 
                                                 ′ 
                                               
                                               + 
                                               h 
                                             
                                             , 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               λ 
                                               0 
                                             
                                             + 
                                             π 
                                             - 
                                             
                                               2 
                                                
                                               
                                                   
                                               
                                                
                                               γ 
                                             
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                             
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 v 
                               
                               < 
                               0 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       w 
                                       2 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   
                                     P 
                                     S 
                                   
                                    
                                   
                                     ( 
                                     
                                       u 
                                       , 
                                       
                                         v 
                                         + 
                                         h 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               , 
                             
                           
                           
                             
                                 
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         w 
                         1 
                       
                     
                     = 
                     
                       
                         
                           v 
                           
                             v 
                             + 
                             h 
                           
                         
                          
                         
                           
 
                         
                          
                         
                           w 
                           2 
                         
                       
                       = 
                       
                         - 
                         
                           
                             2 
                              
                             v 
                              
                             
                                 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             u 
                           
                           h 
                         
                       
                     
                   
                   , 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 ′ 
                               
                               = 
                               
                                 v 
                                 
                                   
                                     cos 
                                     2 
                                   
                                    
                                   u 
                                 
                               
                             
                           
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               a 
                                
                               
                                   
                               
                                
                               cylindrical 
                                
                               
                                   
                               
                                
                               x 
                                
                               
                                 - 
                               
                                
                               ray 
                                
                               
                                   
                               
                                
                               detector 
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                         w 
                         2 
                       
                     
                     = 
                     
                       
                         - 
                         
                           
                             2 
                              
                             v 
                           
                           h 
                         
                       
                        
                       
                         
                           SDD 
                           2 
                         
                         
                           
                             SDD 
                             2 
                           
                           + 
                           
                             u 
                             2 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       v 
                       ′ 
                     
                     = 
                     
                       v 
                        
                       
                         
                           
                             
                               SDD 
                               2 
                             
                             + 
                             
                               u 
                               2 
                             
                           
                           
                             SDD 
                             2 
                           
                         
                       
                        
                       
                           
                       
                        
                       for 
                        
                       
                           
                       
                        
                       a 
                        
                       
                           
                       
                        
                       flat 
                        
                       
                           
                       
                        
                       x 
                        
                       
                         - 
                       
                        
                       ray 
                        
                       
                           
                       
                        
                       detector 
                     
                   
                 
               
             
           
         
       
     
     where P C (u, v, λ) is said circle data, P S (u, z) is said scanogram data, w 1  and w 2  are weighting factors. 
   
   
       26 . A medium as recited in  claim 25 , wherein said method comprises:
 estimating said line data using   
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       27 . A medium as recited in  claim 24 , wherein said method comprises:
 estimating said line data using   
     
       
         
           
             
               
                 P 
                 LF 
               
                
               
                 ( 
                 
                   u 
                   , 
                   v 
                   , 
                   h 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 2 
               
                
               
                 ( 
                 
                   1 
                   + 
                   
                     cos 
                      
                     
                       
                         h 
                          
                         
                             
                         
                          
                         π 
                       
                       d 
                     
                   
                 
                 ) 
               
               × 
               
                 
                   P 
                   L 
                 
                  
                 
                   ( 
                   
                     u 
                     , 
                     v 
                     , 
                     h 
                   
                   ) 
                 
               
             
           
         
       
     
   
   
       28 . A medium as recited in  claim 25 , wherein said weighting factors comprise
     w   1S =3 w   1   2 −2 w   1   3 .       w   2S =3 w   2   2 −2 w   2   3 .   
   
   
       29 . A medium as recited in  claim 23 , wherein said method comprises estimating said line data using multiple scanogram rays for each estimated line ray. 
   
   
       30 . A medium as recited in  claim 23 , wherein said method comprises estimating said line data using one of local smoothing and adaptive filtering. 
   
   
       31 . A medium as recited in  claim 23 , wherein said reconstructing comprises one of filtered backprojection type reconstruction and backprojection filtration type reconstruction. 
   
   
       32 . A medium as recited in  claim 23 , wherein said reconstructing comprises reconstruction of full revolution circular data. 
   
   
       33 . A medium as recited in  claim 23 , wherein said reconstructing comprises reconstruction of partial revolution circular data.

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