Image Sparse Representation And Compression Coding Method With Bandelet Transform

Bandelet bases lead to optimal sparse representation for geometrically regular images and have potential power for the application of image compression. Based on the theories of the first generation Bandelet transform introduced by Pennec and Mallat, and the second generation Bandelet transform introduced by Peyre and Mallat, two corresponding image compression coding strategies are derived in this paper. The main works are as follows: (1) Based on a deep research on the first generation Bandelet transform, a context model of Bandelet coefficients for image compression is proposed, and then an adaptive arithmetic coding procedure is performed. Experimental results show that the model is effective in image compression, especially to images having regular geometric structures. (2) With a deep research on the second generation Bandelet transform, the complexity of the second generation Bandelet transform algorithm is analized and several strategies are introduced to reduce the complexity. Using progressive image compressing method and EBCOT algorithm, an embedded block coding method corresponding to the second generation bandelet transform is derived. The second generation bandelet coder is fidelity progressive and resolution progressive, which is suitable for data transformation on the internet. Comparisons are made with JPEG2000. Experimental results show that the second generation bandelet compressed images keep a regular geometry along the direction of the computed geometric flow and have a better visual quality than JPEG2000 compressed images.