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Parametrized quasi-soft thresholding operator for compressed sensing and matrix completion. (English) Zbl 1442.65078

Summary: Compressed sensing and matrix completion are two new approaches to signal acquisition and processing. Even though the two approaches are different, there is a close connection between them. We introduce a parametrized quasi-soft thresholding operator and use it to obtain new algorithms for compressed sensing and matrix completion. Furthermore, by updating the parametrized quasi-soft thresholding operator in every iteration, the varied parametric quasi-soft thresholding algorithm is obtained. The convergence of the algorithms is analyzed, and numerical results show that the new algorithms can effectively improve the accuracy.

MSC:

65F55 Numerical methods for low-rank matrix approximation; matrix compression
15A83 Matrix completion problems
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