Blind Deconvolution Using a Regularized Structured Total Least Norm Algorithm

Abstract

Rosen, Park, and Glick proposed the structured total least norm (STLN) algorithm for solving problems in which both the matrix and the right-hand side contain errors. We extend this algorithm for ill-posed problems by adding regularization, and we use the resulting algorithm to solve blind deconvolution problems as encountered in image deblurring when both the image and the blurring function have uncertainty. The resulting regularized structured total least norm (RSTLN) algorithm preserves any affine structure of the matrix and minimizes a discrete $\ell_p$-norm measure of the error, where p=1, 2, or $\infty$. We demonstrate the effectiveness of these algorithms for blind deconvolution.