All phase biorthogonal transform and its application in JPEG-like image compression

This paper proposes new concepts of the all phase biorthogonal transform (APBT) and the dual biorthogonal basis vectors. In the light of all phase digital filtering theory, three kinds of all phase biorthogonal transforms based on the Walsh transform (WT), the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT) are proposed. The matrices of APBT based on WT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT. Compared with DCT-based JPEG (DCT-JPEG) image compression algorithm at the same bit rates, the PSNR and visual quality of the reconstructed images using these transforms are approximate to DCT, outgoing DCT-JPEG at low bit rates especially. But the advantage is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation easier.