Wavelet Transforms and Multiscale Estimation Techniques for the Solution of Multisensor Inverse Problems
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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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 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 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 differing 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 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.
- Numerical Mathematics