An Overview of Wavelet Based Multiresolution Analyses
Bjorn D. Jawerth, Wim Sweldens · SIAM Review · 1994
In this paper an overview of wavelet based multiresolution analyses is presented. First, the continuous wavelet transform in its simplest form is discussed. Then, the definition of a multiresolution analysis is given and how wavelets fit into it is shown. The authors 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.