4x4 transform for media coding

Abstract

In general, techniques are described that provide for 4×4 transforms for media coding. A number of different 4×4 transforms are described that adhere to these techniques. As one example, an apparatus includes a 4×4 discrete cosine transform (DCT) hardware unit. The DCT hardware unit implements an orthogonal 4×4 DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (ξ) such that the scaled factor equals a square root of a sum of a square of the first internal factor (C) plus a square of the second internal factor (S). The 4x4 DCT hardware unit applies the 4x4 DCT implementation to media data to transform the media data from a spatial domain to a frequency domain. As another example, an apparatus implements a non-orthogonal 4×4 DCT to improve coding gain.

1 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (ξ) such that the scaled factor equals a square root of a sum of a square of the first internal factor (C) plus a square of the second internal factor (S), the first and second internal factors (C, S) are co-prime and greater than or equal to two; and   a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients.   
     
     
         2 . The apparatus of  claim 1 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         3 . The apparatus of  claim 2 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         4 . The apparatus of  claim 1 , wherein the block transform unit is configured to apply an orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         5 . The apparatus of  claim 4 , wherein the block transform unit is configured to apply the four point DCT in a row dimension and apply the four point DCT in a column dimension. 
     
     
         6 . The apparatus of  claim 1 , wherein the block transform unit applies first and second internal factors (C, S), wherein (C, S) equals one of (2, 5), (3, 7), (5, 12), and (17, 41). 
     
     
         7 . The apparatus of  claim 1 , wherein the DCT is a type II DCT. 
     
     
         8 . The apparatus of  claim 1 , wherein the block transform unit comprises a processor configured to execute software to apply the DCT of the orthogonal 4 point DCT. 
     
     
         9 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (ξ) such that the scaled factor equals a square root of a sum of a square of the first internal factor (C) plus a square of the second internal factor (S), the first and second internal factors (C, S) are dyadic rational numbers; and   a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients.   
     
     
         10 . The apparatus of  claim 9 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         11 . The apparatus of  claim 10 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         12 . The apparatus of  claim 9 , wherein the block transform unit is configured to apply a 4×4 DCT of a substantially orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         13 . The apparatus of  claim 12 , wherein the block transform unit is configured to apply the four point DCT in a row dimension and apply the four point DCT in a column dimension 
     
     
         14 . The apparatus of  claim 9 , wherein the DCT is a type II DCT. 
     
     
         15 . The apparatus of  claim 9 , wherein the block transform unit comprises a processor configured to execute software to apply the 4 point DCT. 
     
     
         16 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (ξ) by the following equation:   
       
         
           
             
               ξ 
               = 
               
                 
                   C 
                   + 
                   S 
                 
                 
                   ω 
                   + 
                   ψ 
                 
               
             
           
         
         wherein variables ω and ψ denote irrational internal transform factors and variables C and S denote internal transform factors used in place of variables ω and ψ in integer implementations of the non-orthogonal 4×4 DCT, the first and second internal factors (C, S) are co-prime and greater than or equal to two; and 
         a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients. 
       
     
     
         17 . The apparatus of  claim 16 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         18 . The apparatus of  claim 17 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         19 . The apparatus of  claim 16 , wherein the block transform unit is configured to apply an orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         20 . The apparatus of  claim 19 , wherein the block transform unit is configured to apply the four point DCT in a row dimension and apply the four point DCT in a column dimension. 
     
     
         21 . The apparatus of  claim 16 , wherein the block transform unit applies first and second internal factors (C, S), wherein (C, S) equals one of (2, 5), (3, 7), (5, 12), and (17, 41). 
     
     
         22 . The apparatus of  claim 16 , wherein the DCT is a type II DCT. 
     
     
         23 . The apparatus of  claim 16 , wherein the block transform unit comprises a processor configured to execute software to apply the DCT of the orthogonal 4 point DCT. 
     
     
         24 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (ξ) by the following equation:   
       
         
           
             
               ξ 
               = 
               
                 
                   C 
                   + 
                   S 
                 
                 
                   ω 
                   + 
                   ψ 
                 
               
             
           
         
         wherein variables ω and ψ denote irrational internal transform factors and variables C and S denote internal transform factors used in place of variables ω and ψ in integer implementations of the non-orthogonal 4×4 DCT, the first and second internal factors (C, S) are dyadic rational numbers; and 
         a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients. 
       
     
     
         25 . The apparatus of  claim 24 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         26 . The apparatus of  claim 25 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         27 . The apparatus of  claim 24 , wherein the block transform unit is configured to apply a 4×4 DCT of a substantially orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         28 . The apparatus of  claim 27 , wherein the block transform unit is configured to apply the four point DCT in a column dimension and apply the four point DCT in a row dimension. 
     
     
         29 . The apparatus of  claim 24 , wherein the DCT is a type II DCT. 
     
     
         30 . The apparatus of  claim 24 , wherein the block transform unit comprises a processor configured to execute software to apply the 4 point DCT. 
     
     
         31 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (A, B) as a part of the 4×4 inverse DCT that are related to a scaled factor (ξ) by the following equation:   
       
         
           
             
               
                 ξ 
                 = 
                 
                   
                     A 
                     + 
                     B 
                   
                   
                     1 
                     + 
                     
                       1 
                        
                       
                         / 
                       
                        
                       
                         2 
                       
                     
                   
                 
               
               , 
             
           
         
         wherein the scaled factor (ξ) equals a sum of the first internal factor (A) plus the second internal factor (B) divided by one plus one divided by the square root of two, the first and second internal factors (A, B) are co-prime and greater than or equal to two; and 
         a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients. 
       
     
     
         32 . The apparatus of  claim 31 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         33 . The apparatus of  claim 32 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         34 . The apparatus of  claim 31 , wherein the block transform unit is configured to apply an orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         35 . The apparatus of  claim 34 , wherein the block transform unit is configured to apply the four point DCT in a row dimension and apply the four point DCT in a column dimension. 
     
     
         36 . The apparatus of  claim 31 , wherein the block transform unit applies first and second internal factors (A, B), wherein (A, B) equals one of (3, 2), (7, 5), and (29, 41). 
     
     
         37 . The apparatus of  claim 31 , wherein the DCT is a type II DCT. 
     
     
         38 . The apparatus of  claim 31 , wherein the block transform unit comprises a processor configured to execute software to apply the DCT of the orthogonal 4 point DCT. 
     
     
         39 . An apparatus for encoding media data comprising:
 a block transform unit configured to apply a 4 point discrete cosine transform (DCT) to determine one or more transform coefficients, the 4 point DCT having an odd portion that applies first and second internal factors (A, B) as a part of the 4×4 inverse DCT that are related to a scaled factor (ξ) by the following equation:   
       
         
           
             
               
                 ξ 
                 = 
                 
                   
                     A 
                     + 
                     B 
                   
                   
                     1 
                     + 
                     
                       1 
                        
                       
                         / 
                       
                        
                       
                         2 
                       
                     
                   
                 
               
               , 
             
           
         
         wherein the scaled factor (ξ) equals a sum of the first internal factor (A) plus the second internal factor (B) divided by one plus one divided by the square root of two, the first and second internal factors (A, B) are dyadic rational numbers; and 
         a quantization unit configured to determine one or more quantized transform coefficients based on the one or more transform coefficients. 
       
     
     
         40 . The apparatus of  claim 39 , wherein determining the one or more quantized transform coefficients comprises scaling the one or more transform coefficients. 
     
     
         41 . The apparatus of  claim 40 , wherein scaling comprises multiplying the transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         42 . The apparatus of  claim 39 , wherein the block transform unit is configured to apply a 4×4 DCT of a substantially orthogonal 4×4 DCT by applying the four point DCT. 
     
     
         43 . The apparatus of  claim 42 , wherein the block transform unit is configured to apply the four point DCT in a column dimension and apply the four point DCT in a row dimension. 
     
     
         44 . The apparatus of  claim 39 , wherein the DCT is a type II DCT. 
     
     
         45 . The apparatus of  claim 39 , wherein the block transform unit comprises a processor configured to execute software to apply the 4 point DCT.