Computing optimal low-rank matrix approximations for image processing

In this work, we describe a new framework for solving inverse problems, where training data is used, as a substitute for the forward model, to compute an optimal low-rank regularized inverse matrix directly, allowing for very fast computation of a regularized solution. An empirical Bayes risk minimization framework will be used to incorporate training data and to formulate the problem of computing an optimal low-rank regularized inverse matrix. We describe some theoretical results that motivate the development of numerical methods for computing an optimal low-rank regularized inverse matrix and demonstrate our approach on examples from image deconvolution.