Deconvolution Using Meyer Wavelets

Abstract

In this paper, we have a procedure based on band limited orthogonal wavelets, the Meyer wavelets, to solve convolution equations of the first kind, which is usually an ill-posed problem. The problem will be converted into a well-posed problem in the scaling subspaces, provided that the kernel k L 1 (R) and k() = 0. In the case k() has a single zero, we search for a solution in the wavelet subspaces, which can be used to solve the problem numerically. Results related to the convergence rate and error bounds are obtained. However, the stability of the discrete system depends on the resolution level m.