Image compression by sparse PCA coding in curvelet domain

Abstract

This paper uses the newly developed concept of ‘sparsity’ in signal processing to the context of Image Compression. The first step of the scheme is to use a sparsifying transform on the image. The sparse set of coefficients is encoded via Sparse PCA. Wavelet Transform had been used profusely for image compression tasks. But the choice is not the ideal one. The partial reconstruction error from wavelet coefficients is an order of magnitude higher than the ideal error rate. In this paper image compression is carried in the curvelet domain—a better choice compared to wavelets, at least theoretically, since the reconstruction error rate with curvelet coefficients is of the same asymptotic order as that of the ideal error rate. The compression scheme is tested on the Lena and Barbara image as well as the USPS and Yale Face databases.