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Zbl 1133.65022
Elad, Michael; Matalon, Boaz; Zibulevsky, Michael
Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization. (English)
[J] Appl. Comput. Harmon. Anal. 23, No. 3, 346-367 (2007). ISSN 1063-5203

The authors consider the problem of linear least squares with non-quadratic regularization (RLS) in the form: minimize $\{ \|Az - b\|^2 + \rho (z) \}$, for $z \in\Bbb R^n$, where $A$ is an $m \times n, (m < n)$ full rank matrix. They prove that for this problem the parallel coordinate descent algorithm (previously proposed by one of the authors), the expectation-maximization one and a shrinkage minimization method are essentially equivalent for the numerical solution of the RLS problem. Some image denoising numerical experiments are also presented.
[Constantin Popa (Constanţa)]

MSC 2000:: *65F20 Overdetermined systems (numerical linear algebra)

Keywords: least squares; regularization; inverse problems; denoising; shrinkage; basis pursuit; sparsity; coordinate-descent; proximal point; numerical experiments

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