Wavelets and their applications

The aim of this review is to provide a practical guide for those considering the application of the discrete wavelet transform in their computational practice. The concept of a wavelet is introduced and its applications, computational and otherwuse, are described in brief, the reader being referred to the literature for the rigorous proof of the mathematical statements used. The multiresolution analysis and the fast wavelet transform have become virtually synonymous to the discrete wavelet transform. The correct choice of a wavelet and the use of nonstandard matrix multiplication often prove crucial for the solution of a problem. at hand. The wavelet analysis reveals such characteristics of a function as its fractal properties and singularities, among others. Applying the wavelet transform to operator expressions is helpful in solving certain types of equations. In dealing with discretized functions - as one often does in practical applications - the stability of the wavelet transform and of related numerical algorithms becomes a problem. Following the discussion of all the above topics, practical applications of the wavelet analysis are illustrated, which are, however, too numerous for us to cover more than a tiny part of them. The authors would appreciate any comments which would better this review and bring it nearer to the goal formulated in the first phrase of this abstract.