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Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization. (English) Zbl 1133.65022
The authors consider the problem of linear least squares with non-quadratic regularization (RLS) in the form: minimize $\left\{\parallel Az-b{\parallel }^{2}+\rho \left(z\right)\right\}$, for $z\in {ℝ}^{n}$, where $A$ is an $m×n,\left(m 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.
##### MSC:
 65F20 Overdetermined systems, pseudoinverses (numerical linear algebra)