The algorithm of APBT is similar to the conventional DCT.
The essence of DCT, APBT and their inverse transform is the matrix multiplication, as shown in Eqs.
In the parallel algorithm of APBT, every thread executes vector multiplication twice, then every thread gets an APBT coefficient.
APBT removes the correlation between pixels in each sub-image; it provides necessary conditions for image compression.
In the serial algorithm of APBT and quantization, the pixels of source image are processed in order.
After threads execute the code of APBT and quantization completely, the block will get an 8 x 8 coefficient matrix.
APBT and quantization are prepared for image compression, and the image data is further compressed by entropy coding.
When Zig-zag ordering, every thread compares its quantized APBT coefficient with zero, if the coefficient is not equal to zero, we put the number of the thread in the array.
While the encoder is completed, the parallel algorithm of inverse APBT and quantization is similar to parallel APBT and quantization.
12 and Table 3, we can know the efficiency of parallel APBT algorithm is much higher than serial APBT algorithm.
So the efficiency problem of conventional APBT algorithm and the blocking artifacts in DCT can be solved by the parallel APBT algorithm.