Blind Deconvolution: A Matter of Norm
Computing in Science and Engineering
Overview of total least-squares methods
Signal Processing
Fast robust regression algorithms for problems with Toeplitz structure
Computational Statistics & Data Analysis
Structured least squares problems and robust estimators
IEEE Transactions on Signal Processing
Fast deconvolution with approximated PSF by RSTLS with antireflective boundary conditions
Journal of Computational and Applied Mathematics
Constrained numerical optimization methods for blind deconvolution
Numerical Algorithms
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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.