Wavelet moment method for the Cauchy problem for the Helmholtz equation

The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from inexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the moment problem that is equivalent to a Cauchy problem for the Helmholtz equation. A method of regularization by projection with application of the Meyer wavelet it Cauchy problem Helmholtz equation. A method of regularization by projection with application of the Meyer wavelet subspaces is introduced and analyzed. The dericed formula, describing the projection level in term Cauchy data, allows us to prove the convergence and stability of the method. (C) 2008 Elsevier B.V. All rights reserved.