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A unifying analysis of projected gradient descent for -constrained least squares
- Source :
-
Applied & Computational Harmonic Analysis . May2013, Vol. 34 Issue 3, p366-378. 13p. - Publication Year :
- 2013
-
Abstract
- Abstract: In this paper we study the performance of the Projected Gradient Descent (PGD) algorithm for -constrained least squares problems that arise in the framework of compressed sensing. Relying on the restricted isometry property, we provide convergence guarantees for this algorithm for the entire range of , that include and generalize the existing results for the iterative hard thresholding algorithm and provide a new accuracy guarantee for the iterative soft thresholding algorithm as special cases. Our results suggest that in this group of algorithms, as p increases from zero to one, conditions required to guarantee accuracy become stricter and robustness to noise deteriorates. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 34
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 85880039
- Full Text :
- https://doi.org/10.1016/j.acha.2012.07.004