Research On All Phase Biothogonal Transform Theory And Its Applications In Image Coding

At present, the orthogonal transform theory has been quite mature, especially the research for DCT which has been developed the most in-depth. However, using orthogonal transformation is not necessarily the optimal choice in image coding. One of its shortcomings is that the quantization table is more complicated. Furthermore, block DCT transform coding has serious blocking artifacts when the image is highly compressed at low bit rate. To solve the above problems, this paper proposes the all phase biorthogonal transform (APBT) on the basis of all phase filtering, and explores its application in image coding. The research of this paper has important theoretical significance and application value. The principal innovation points of this dissertation are as follows:(1) Proposed new concepts of the all phase biorthogonal transform and the dual basis vectors on the basis of all phase sequency filtering. Based on Walsh-Hadamard transform (WHT), DCT, and IDCT, the mathematical expression of the APBT matrices with arbitrary order is derived and the properties of the APBT matrices are analyzed. The basis image of APBT is given and the energy distribution characteristic of the basis image is analyzed.(2) Proposed JPEG-like image coding algorithms based on the APBT and the directional APBT. In the APBT-based JPEG-like image coding algorithm, APBT can be used as the new transform instead of DCT which adopted in the conventional JPEG compression algorithm. Accordingly, in the quantization step, the uniform quantization is used instead of the complex quantization table. Compared with the traditional JPEG algorithm, better objective quality and subjective effects are achieved at the low bit rate. In addition, for the removal of the blocking artifacts appearing in the reconstructed image at low bit rate, an effective deblocking algorithm is applied. On the research of directional DCT and its application in image coding, the image coding algorithm based on the directional APBT is proposed, considering other directions apart from the horizontal and vertical ones. For images with more direction details, good compression is achieved.(3) In the light of wavelet-based SPIHT coding algorithm, APBT-based embedded image coding algorithm is proposed. Better performance is obtained than JPEG compression at low bit rate. The advantage of the algorithm is that its bit rate is precisely controlled; initially explored APBT domain vector quantization encoding and achieves better compression results than scalar quantization coding, further expanding the applications of APBT in image coding.(4) Proposed the low bit-rate block coding algorithm based on DCT, APBT and warped DCT, using the all phase DCT low-pass filter with good low-pass characteristics and the all phase extended DCT interpolation with good interpolation performance. Considering the features of the Bayer pattern color image, Bayer pattern color image compression algorithm is proposed based on 9/7 wavelet transform and all phase interpolation. Simulation results show that the algorithm presented in this paper is more suitable to the Bayer pattern image compression.