Volume 40, pp. 356-372, 2013.

Solving regularized linear least-squares problems by the alternating direction method with applications to image restoration

Jianjun Zhang and Benedetta Morini

Abstract

We present and analyze ways to apply the Alternating Direction Method (ADM) to bound-constrained quadratic problems including $\ell_1$ and $\ell_2$ regularized linear least-squares problems. The resulting ADM schemes require the solution of two subproblems at each iteration: the first one is a linear system, the second one is a bound-constrained optimization problem with closed-form solution. Numerical results on image deblurring problems are provided and comparisons are made with a Newton-based method and a first-order method for bound-constrained optimization.

Full Text (PDF) [308 KB]

Key words

Linear least-squares problems, $\ell_1$ and $\ell_2$ regularization, bound-constraints, alternating direction method, image deblurring.

AMS subject classifications

65F22, 65K10, 65T50, 68U10, 90C25

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