Sparse Representation through Multi-Resolution Transform for Image Coding

Having a compact basis is useful both for compression and fordesigning efficient numerical algorithms. In this paper, a newimage coding scheme using a multi-resolution transform knownas Bandelet Transform that provides an optimally compact basisfor images by exploring their directional characteristics isproposed. As this process results in a sparse representation,Zero Vector Pruning is applied in-order to extract the non-zerocoefficients. Further the geometric interpixel redundanciespresent in the transformed coefficients are removed. Thepsycho-visual redundancies are removed using simple VectorQuantization (VQ) process. Finally, Huffman encoder is used toencode the significant coefficients. The proposed compressionmethod beats the standard wavelet based algorithms in terms ofmean-square-error (MSE) and visual quality, especially in thelow-rate compression regime. A gain in the bit-rate of about0.81 bpp over the wavelet based algorithms is achieved yieldingsimilar quality factor.