Natural Thresholding Algorithms for Signal Recovery With Sparsity

The algorithms based on the technique of optimal <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding metho...

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Bibliographic Details
Published in:IEEE open journal of signal processing Vol. 3; pp. 417 - 431
Main Authors: Zhao, Yun-Bin, Luo, Zhi-Quan
Format: Journal Article
Language:English
Published: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Compressed sensing
Computational efficiency
Computing costs
concave minimization
Concavity
Indexes
Matching pursuit algorithms
Mathematical models
Optimization
Recovery
regularization method
restricted isometry property
Signal processing
Signal processing algorithms
Signal reconstruction
signal recovery
thresholding algorithms
ISSN:2644-1322, 2644-1322
Online Access:Get full text
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Summary:The algorithms based on the technique of optimal <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for OT-based algorithms remains high at the current stage of their development. This stimulates the development of the so-called natural thresholding (NT) algorithm and its variants in this paper. The family of NT algorithms is developed through the first-order approximation of the so-called regularized optimal <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-thresholding model, and thus the computational cost for this family of algorithms is significantly lower than that of the OT-based algorithms. The guaranteed performance of NT-type algorithms for signal recovery from noisy measurements is shown under the restricted isometry property and concavity of the objective function of regularized optimal <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-thresholding model. Empirical results indicate that the NT-type algorithms are robust and very comparable to several mainstream algorithms for sparse signal recovery.
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ISSN:2644-1322
2644-1322
DOI:10.1109/OJSP.2022.3195115