Unmatched Preconditioning of the Proximal Gradient Algorithm

This work addresses the resolution of penalized least-squares problems using the proximal gradient algorithm (PGA). PGA can be accelerated by preconditioning strategies. However, typical effective choices of preconditioners may correspond to intricate matrices that are not easily inverted, leading t...

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Vydáno v:IEEE signal processing letters Ročník 29; s. 1122 - 1126
Hlavní autoři: Savanier, Marion, Chouzenoux, Emilie, Pesquet, Jean-Christophe, Riddell, Cyril
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Témata:
Algorithms
Computed tomography
Convergence
convergence analysis
Electronics packaging
Engineering Sciences
Image reconstruction
Iterative methods
Linear programming
matrix approximation
Measurement
Preconditioning
proximal methods
Signal and Image processing
Signal processing algorithms
Matrix approximation
Computed tomography
Proximal methods
Image reconstruction
Convergence analysis
ISSN:1070-9908, 1558-2361
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Shrnutí:This work addresses the resolution of penalized least-squares problems using the proximal gradient algorithm (PGA). PGA can be accelerated by preconditioning strategies. However, typical effective choices of preconditioners may correspond to intricate matrices that are not easily inverted, leading to increased complexity in the computation of the proximity step. To relax these requirements, we propose an unmatched preconditioning approach where two metrics are used in the gradient step and the proximity step. We provide convergence conditions for this new iterative scheme and characterize its limit point. Simulations for tomographic image reconstruction from undersampled measurements show the benefits of our approach for various simple choices of metrics.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2022.3169088