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ParNes: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals. (English) Zbl 1284.65055

This article develops an algorithm for underdetermined least squares problems with 1-norm constraint on the solution. It relies on a modified Nestorev method that periodically updates the prox-center optimally and renders the proposed method almost always linearly convergent. The method is then applied to find the minimum 1-norm solution to an underdetermined least squares problem when teamed with the Pareto root finder. Numerical tests show that these methods achieve comparable numerical results in comparable time for such a problem in image processing and other areas of application.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F50 Computational methods for sparse matrices
65K05 Numerical mathematical programming methods
90C25 Convex programming
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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