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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 $\{ \|Az - b\|^2 + \rho (z) \}$, 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.

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65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
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