Wavelet Transforms and Multiscale Estimation Techniques for the Solution of Multisensor Inverse Problems

The application of multiscale and stochastic techniques to the solution of linear inverse problems is presented. This approach allows for the explicit and easy handling of a variety of diiculties commonly associated with problems of this type. Regularization is accomplished via the incorporation of prior information in the form of a multiscale stochastic model. We introduce the relative error covariance matrix (RECM) as a tool for quantitatively evaluating the manner in which data contributes to the structure of a reconstruction. In particular, the use of a scale space formulation is ideally suited to the fusion of data from several sensors with diiering resolutions and spatial coverage (eg. sparse or limited availability). Moreover, the RECM both provides us with an ideal tool for understanding and analyzing the process of multisensor fusion and allows us to deene the space-varying optimal scale for reconstruction as a function of the nature (resolution, quality, and coverage) of the available data. Examples of our multiscale maximum a posteriori inversion algorithm are demonstrated using a two channel deconvolution problem.