Data Compression

Abstract

An important application of the orthogonal transforms is data compression. The key to securing data compression is signal representation, which concerns the representation of a given class (or classes) of signals in an efficient manner. If a discrete signal is comprised of N sampled values, then it can be thought of as being a point in an N-dimensional space. Each sampled value is then a component of the data N-vector X which represents the signal in this space. For more efficient representation, one obtains an orthogonal transform of X which results in Y = TX, where Y and T denote the transform vector and transform matrix respectively. The objective is to select a subset of M components of Y, where M is substantially less than N. The remaining (N — M) components can then be discarded without introducing objectionable error, when the signal is reconstructed using the retained M components of Y. The orthogonal transforms must therefore be compared with respect to some error criterion. One such often used criterion is the mean-square error criterion.