A MULTISCALE APPROACH TO SENSOR FUSION AND THE SOLUTION OF LINEAR INVERSE PROBLEMS

The application of multiscale and stochastic techniques to the solution of linear inverse problems is presented. This approach allows for explicit and easy handling of a variety of difficulties 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 contribute 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 differing resolutions and spatial coverage (e.g., 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 define 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 formulated to illustrate many of the features associated with more general linear inverse problems. (C) 1995 Academic Press, Inc.