Digital Image Restoration
Blind Deconvolution Using a Regularized Structured Total Least Norm Algorithm
SIAM Journal on Matrix Analysis and Applications
A Nonnegatively Constrained Convex Programming Method for Image Reconstruction
SIAM Journal on Scientific Computing
Covariance-Preconditioned Iterative Methods for Nonnegatively Constrained Astronomical Imaging
SIAM Journal on Matrix Analysis and Applications
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Iterative Identification and Restoration of Images (The International Series in Engineering and Computer Science)
Journal of Computational and Applied Mathematics
High-Performance Three-Dimensional Image Reconstruction for Molecular Structure Determination
International Journal of High Performance Computing Applications
An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems
SIAM Journal on Scientific Computing
Implicit Filtering
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This paper describes a nonlinear least squares framework to solve a separable nonlinear ill-posed inverse problem that arises in blind deconvolution. It is shown that with proper constraints and well chosen regularization parameters, it is possible to obtain an objective function that is fairly well behaved and the nonlinear minimization problem can be effectively solved by a Gauss---Newton method. Although uncertainties in the data and inaccuracies of linear solvers make it unlikely to obtain a smooth and convex objective function, it is shown that implicit filtering optimization methods can be used to avoid becoming trapped in local minima. Computational considerations, such as computing the Jacobian, are discussed, and numerical experiments are used to illustrate the behavior of the algorithms. Although the focus of the paper is on blind deconvolution, the general mathematical model addressed in this paper, and the approaches discussed to solve it, arise in many other applications.