This paper proposes a new discrete transform called AP-Contourlet (All Phase Contourlet). Contourlet is a flexible and fixed transform for image representations of geometrical regularity. Because it has been concluded that APDCT (All Phase DCT) filter and APIDCT (All Phase IDCT) are excellent respectively in subband decomposition and image interpolation, this paper develops a novel mutliscale decomposition method based on the APDCT filter and APIDCT interpolators to replace Laplacian Pyramid at the fist step of contoulet. Experiments in denoising typical images have shown the performance of the proposed AP-contourlet is obviously superior to original contourlet both in vision and in signal to noise ratio (SNR).
This paper proposes a novel hierarchical coding algorithm based on the All Phase IDCT (APIDCT) interpolation. The All Phase Digital Filter (APDF) is a new type of linear phase filter. For a data vector with a length of N obtained by blocking a signal, there are N different phase data blocks that include the same sampling point. Through taking the mean of the N values as the filtering output, the APDF can eliminate different meanings of the orthogonal transform filtering values of those data vectors and thereby the block effect. According to this idea, this paper deduces the formula of two-dimension APIDCT. Then, this paper compares the performances of several kinds of APDF and demonstrates that the APIDCT filter has the best performance in image interpolation. By combining the interpolation with multi-subsampling and adaptive arithmetic coding, a simple hierarchical image-coding algorithm is shaped up. This technique can be used to scalable coding in spatial resolution. The simulation results show that the compression ratio and restored image quality better than JPEG compression can be achieved by only three layers, and no block effect has been found even in high compression ratio.