SVD-Wavelet Algorithm for image compression

We explore the use of the singular value decomposition (SVD) in image compression. We link the SVD and the multiresolution algorithms. In [22] it is derived a multiresolution representation of the SVD decomposition, and in [15] the SVD algorithm and Wavelets are linked, proposing a mixed algorithm which roughly consist on applying firstly a discrete Wavelet transform and secondly the SVD algorithm to each subband. We propose a new algorithm, which is carried out in two main steps. Firstly we decompose the data matrix corresponding to the image following a singular value decomposition. Secondly we apply a Harten’s multiresolution decomposition to the singular vectors which are considered significant. We study the compression capabilities of this new algorithm. We also propose a variant of the implementation, where the multiresolution transformation is carried out by blocks. We apply on each block, depending on a selection process, either the algorithm presented or the 2D multiresolution algorithm based on biorthogonal wavelets.