Regularization of an inverse problem for potential field

This paper discusses the Cauchy problem for Laplace equation. i,e.. a class of inverse problems for potential field [GRAPHICS] which has been formulated from geophysics. such as gravity and magnetic prospecting. The problem is well known to be severely ill-posed, that is, a small error in the Cauchy data may give rise to a dramatically large perturbation in the solution, The authors use a so-called regularization method that if the Cauchy data are given roughly then one can mollify them by the elements of an appropriate m-regular multiresolution approximation {(V) over tilde(j)}(j-z) of L-2(R-2) which is generated by the wavelength of Meyer. Within (j) over tilde the problem is well posed, and one call find a mollification parameter J depending on the noise level epsilon in the Cauchy data such that the error estimation between the exact solution and the mollification is of H square lder type.