Regularized wavelets for solving inverse ill-posed problems

This paper describes regularized wavelets and numerical algorithms for a regularized wavelet-analysis based on the bayes strategy. This program includes the investigation of a possibility for finding a basis in terms of a multiresolution analysis under condition that a scaling function would satisfy the properties of a regularization operator and an orthonormal basis simultaneously. Examples of application of the regularized wavelets in the differentiation of composite simulated spectra with a fractal noise are considered.