A MULTIRESOLUTION METHOD FOR DISTRIBUTED PARAMETER-ESTIMATION

A multiresolution method for distributed parameter estimation (or inverse problems) is studied numerically. The identification of the coefficient of an elliptic equation in one dimension is considered as our model problem. First, multiscale bases are used to analyze the degree of ill-posedness of the inverse problem. Second, based on some numerical results, it is shown that the method of scale-by-scale multiresolution yields robust and fast convergence. Finally, it is shown how the method gives a natural regularization approach which is complementary to Tikhonov's regularization.