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 4×4 DCT hardware unit applies the 4×4 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 decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point discrete cosine transform (DCT) to the plurality of reconstructed transform coefficients to produce a residual block, the IDCT having an odd portion that applies first and second internal factors (C, S) that are related to the 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.   
     
     
         2 . The apparatus of  claim 1 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         3 . The apparatus of  claim 2 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         4 . The apparatus of  claim 1 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         5 . The apparatus of  claim 4 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         6 . The apparatus of  claim 1 , wherein the inverse 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 and the IDCT is a type III DCT. 
     
     
         8 . The apparatus of  claim 1 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT. 
     
     
         9 . An apparatus for decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point DCT to the plurality of reconstructed transform coefficients to produce a residual block, the IDCT 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.   
     
     
         10 . The apparatus of  claim 9 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         11 . The apparatus of  claim 10 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         12 . The apparatus of  claim 9 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         13 . The apparatus of  claim 12 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         14 . The apparatus of  claim 9 , wherein the DCT is a type II DCT and the IDCT is a type III DCT. 
     
     
         15 . The apparatus of  claim 9 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT. 
     
     
         16 . An apparatus for decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point discrete cosine transform (DCT) to the plurality of reconstructed transform coefficients to produce a residual block, the IDCT having an odd portion that applies first and second internal factors (C, S) that are related to the 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. 
       
     
     
         17 . The apparatus of  claim 16 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         18 . The apparatus of  claim 17 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         19 . The apparatus of  claim 16 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         20 . The apparatus of  claim 19 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         21 . The apparatus of  claim 19 , wherein the inverse 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 19 , wherein the DCT is a type II DCT and the IDCT is a type III DCT. 
     
     
         23 . The apparatus of  claim 19 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT. 
     
     
         24 . An apparatus for decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point DCT to the plurality of reconstructed transform coefficients to produce a residual block, the IDCT 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 
       
     
     
         25 . The apparatus of  claim 24 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         26 . The apparatus of  claim 25 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         27 . The apparatus of  claim 24 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         28 . The apparatus of  claim 27 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         29 . The apparatus of  claim 24 , wherein the DCT is a type II DCT and the IDCT is a type III DCT. 
     
     
         30 . The apparatus of  claim 24 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT. 
     
     
         31 . An apparatus for decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point discrete cosine transform (DCT) to the reconstructed transform coefficients to produce a residual block, the IDCT having an odd portion that applies first and second internal factors 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. 
       
     
     
         32 . The apparatus of  claim 31 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         33 . The apparatus of  claim 32 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         34 . The apparatus of  claim 31 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         35 . The apparatus of  claim 34 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         36 . The apparatus of  claim 31 , wherein the inverse 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 and the IDCT is a type III DCT. 
     
     
         38 . The apparatus of  claim 31 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT. 
     
     
         39 . An apparatus for decoding media data comprising:
 a reconstruction unit configured to determine a plurality of reconstructed transform coefficients based on a plurality of quantized transform coefficients; and   an inverse transform unit configured to apply an inverse discrete cosine transform (IDCT) of a 4 point DCT to the plurality of reconstructed transform coefficients, the IDCT 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. 
       
     
     
         40 . The apparatus of  claim 39 , wherein determining the plurality of reconstructed transform coefficient comprises scaling the quantized transform coefficients. 
     
     
         41 . The method of  claim 40 , wherein scaling comprises dividing the plurality of reconstructed transform coefficients by a factor based at least on the scaled factor (ξ). 
     
     
         42 . The apparatus of  claim 39 , wherein the inverse transform unit is configured to apply a 4×4 IDCT of a substantially orthogonal 4×4 DCT by applying the four point IDCT. 
     
     
         43 . The apparatus of  claim 42 , wherein the inverse transform unit is configured to apply the four point IDCT in a column dimension and apply the four point IDCT in a row dimension. 
     
     
         44 . The apparatus of  claim 39 , wherein the DCT is a type II DCT and the IDCT is a type III DCT. 
     
     
         45 . The apparatus of  claim 39 , wherein the inverse transform unit comprises a processor configured to execute software to apply the IDCT of the orthogonal 4 point DCT.