Best Basis Selection Using Singular Value Decomposition

Abstract

This paper presents a new idea of best basis selection through singular value decomposition. Wavelet and Wavelet Packet Transform are efficient tools to represent the image. Wavelet Packet Transform is a generalization of wavelet transform which is more adaptive than the wavelet transform because it offers a rich library of bases from which the best one can be chosen for a certain class of images with a specified cost function. Wavelet packet decomposition yields a redundant representation of the image. The problem of wavelet packet image coding consists of considering all possible wavelet packet bases in the library, and choosing the one that gives the best coding performance. In this work, Singular Value Decomposition is used as a tool to select the best basis. Experimental results have demonstrated the validity of the approach.