Lp quasi-norm minimization: algorithm and applications

Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solution...

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Veröffentlicht in:EURASIP journal on advances in signal processing Jg. 2024; H. 1; S. 22 - 28
Hauptverfasser: Sleem, Omar M., Ashour, M. E., Aybat, N. S., Lagoa, Constantino M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2024
Springer
Springer Nature B.V
SpringerOpen
Schlagworte:
Algorithms
Alternating direction method of multipliers
Comparative analysis
Compressed sensing
Continuity (mathematics)
Engineering
Heuristic methods
Iterative methods
Machine learning
Matrix completion
Operators (mathematics)
Optimization
Polynomials
Quantum Information Technology
Rank minimization
Signal processing
Signal reconstruction
Signal,Image and Speech Processing
Sparsity
Spintronics
System identification
Alternating direction method of multipliers
Sparsity
Rank minimization
System identification
Compressed sensing
Matrix completion
Proximal gradient method
ISSN:1687-6180, 1687-6172, 1687-6180
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Zusammenfassung:Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization problems via minimizing the ℓ p quasi-norm, where 0 < p < 1 . An iterative two-block algorithm for minimizing the ℓ p quasi-norm subject to convex constraints is proposed. The proposed algorithm requires solving for the roots of a scalar degree polynomial as opposed to applying a soft thresholding operator in the case of ℓ 1 norm minimization. The algorithm’s merit relies on its ability to solve the ℓ p quasi-norm minimization subject to any convex constraints set. For the specific case of constraints defined by differentiable functions with Lipschitz continuous gradient, a second, faster algorithm is proposed. Using a proximal gradient step, we mitigate the convex projection step and hence enhance the algorithm’s speed while proving its convergence. We present various applications where the proposed algorithm excels, namely, sparse signal reconstruction, system identification, and matrix completion. The results demonstrate the significant gains obtained by the proposed algorithm compared to other ℓ p quasi-norm based methods presented in previous literature.
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ISSN:1687-6180
1687-6172
1687-6180
DOI:10.1186/s13634-024-01114-6