An Overview of Wavelet Based Multiresolution Analyses

In this paper we present an overview of wavelet based multiresolution analyses. First, we brie y discuss the continuous wavelet transform in its simplest form. Then, we give the de nition of a multiresolution analysis and show how wavelets t into it. We take a closer look at orthogonal, biorthogonal and semiorthogonal wavelets. The fast wavelet transform, wavelets on an interval, multidimensional wavelets and wavelet packets are discussed. Several examples of wavelet families are introduced and compared. Finally, the essentials of two major applications are outlined: data compression and compression of linear operators.