We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.

A Reduced Newton Method for Constrained Linear Least-Squares Problems / B. Morini; M. Porcelli; R.H.F. Chan. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 233:(2010), pp. 2200-2212. [10.1016/j.cam.2009.10.006]

A Reduced Newton Method for Constrained Linear Least-Squares Problems

MORINI, BENEDETTA;
2010

Abstract

We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.
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B. Morini; M. Porcelli; R.H.F. Chan
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/366365
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