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

Keywords: Biorthogonal transform Image compression JPEG algorithm All phase biorthogonal transform (APBT) Dual biorthogonal basis vectors Walsh transform (WT) Discrete cosine transform (DCT) Inverse discrete cosine transform (IDCT) Peak signal to noise ratio (PSNR) a b s t r a c t 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 quanti-zation table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation easier. To achieve a greater convenience for image storage and transmission, the development of multimedia and Internet requires a more suitable method for image compression. Discrete cosine transform (DCT) [1] has been adopted widely in international standards for image compression, for example, JPEG [2,3], MPEG-2 [4], MPEG-4 [5] and H.264/AVC [6,7]. In spite of the emerging wavelet-based standard JPEG2000 [8], the DCT-based JPEG standard remains to be the most commonly employed lossy compression algorithm for still images due to its high effectiveness and low computational complexity. In DCT-based lossy image compression algorithm, the quantization table taken into consideration the vision characteristics of human eyes is used. However, adopting different quantization steps for different DCT coefficients makes the quantization table more complex. In particular, more complex multiplications are required when adjusting the bit rates. In this paper, we bring forward a new transform, namely the all phase biorthogonal transform (APBT), which is based on Walsh transform (WT), DCT and inverse discrete cosine transform (IDCT). It can be applied to image compression successfully instead of the conventional DCT. The advantage of the method is that the quantization table is simpler; and the Contents lists available at ScienceDirect