Windowed All Phase Biorthogonal Transform and Its Application in JPEG-Like Image Compression

Abstract

This paper proposes new concepts of the windowed all phase biorthogonal transform (WAPBT), which is inspired by the all phase biorthogonal transform (APBT). In the light of windowed all phase digital filter theory, windowed all phase biorthogonal transforms is proposed. The matrices of WAPBT based on DFT, WHT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT, and the image compression scheme proposed in this paper is called WAPBT-based JPEG (WAPBT-JPEG). With optimal window sequence of WAPBT for image compression obtained by using generalized pattern search algorithm (GPSA), the peak signal to noise ratio (PSNR) and visual quality of the reconstructed images using the WAPBT-JPEG is outgoing DCT-based JPEG (DCT-JPEG) and APBT-based JPEG (APBT- JPEG) approximately at all bit rates. What is more, by comparison with DCT-JPEG, the advantage of proposed scheme 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 is easier. Index Terms—Windowed all phase biorthogonal transform (WAPBT), image compression, discrete cosine transform (DCT), JPEG algorithm, generalized pattern search algorithm (GPSA), windowed all phase digital filter (APDF)