Optimization Online



Anastasia Cornelio(anastasia.cornelio***at***unimore.it)
Elena Loli Piccolomini(elena.loli***at***unibo.it)
James G. Nagy(nagy***at***mathcs.emory.edu)

Abstract: This paper describes a nonlinear least squares framework to solve a separable nonlinear ill-posed inverse problems 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.

Keywords: nonlinear least squares, variable projection, implicit filtering, Tikhonov regularization, blind deconvolution

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 02/12/2012
Entry Accepted: 02/12/2012
Entry Last Modified: 02/12/2012

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