Sparse signal recovery through a modified Dai-Yuan algorithm

Kabiru Ahmed; Mohammed Yusuf Waziri; Mohammed A. Saleh; Abdulgader Z. Almaymuni; Abubakar Sani Halilu; Mohamad Afendee Mohamed; Sulaiman M. Ibrahim; Salisu Murtala; Habibu Abdullahi; Kabiru Ahmed; Mohammed Yusuf Waziri; Mohammed A. Saleh; Abdulgader Z. Almaymuni; Abubakar Sani Halilu; Mohamad Afendee Mohamed; Sulaiman M. Ibrahim; Salisu Murtala; Habibu Abdullahi

doi:10.3934/math.2025877

AIMS Mathematics

2025, Volume 10, Issue 8: 19675-19692. doi: 10.3934/math.2025877

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Research article

Sparse signal recovery through a modified Dai-Yuan algorithm

1.
Department of Mathematics, Bayero University, Kano, Nigeria
2.
Numerical Optimization Research Group, Bayero University, Kano, Nigeria
3.
Department of Cybersecurity, College of Computer, Qassim University, Saudi Arabia
4.
Department of Mathematics, Sule Lamido University, Kafin Hausa, Nigeria
5.
Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, 22200 Terengganu, Malaysia
6.
Mathematical Innovation and Applications Research Group, Sule Lamido University, Kafin Hausa, Nigeria
7.
School of Quantitative Science, Universiti Utara Malaysia, Sintok, Malaysia
8.
Faculty of Education and Arts, Sohar University, Sohar 311, Oman
9.
Department of Mathematics, Federal University, Dutse, Nigeria

Received: 18 May 2025 Revised: 01 August 2025 Accepted: 13 August 2025 Published: 27 August 2025
MSC : 65K10, 68U10

Sparse signal recovery is a concept that is not only central to compressed sensing problems, but also apparent in magnetic resonance imaging (MRI) problems, machine learning, as well as statistical inference. In each of these fields, the target is finding sparse solutions to linear systems of equations that are underdetermined or ill-conditioned. In this paper, an efficient modified Dai-Yuan conjugate gradient method that is globally convergent irrespective of the line search procedure employed was developed to reconstruct sparse signals in compressed sensing. Results of the experiments conducted show that the method is promising.
- compressed sensing,
- conjugate gradient method,
- sparse signals,
- Lipschitz condition,
- global convergence,
- signaling,
- algorithms
Citation: Kabiru Ahmed, Mohammed Yusuf Waziri, Mohammed A. Saleh, Abdulgader Z. Almaymuni, Abubakar Sani Halilu, Mohamad Afendee Mohamed, Sulaiman M. Ibrahim, Salisu Murtala, Habibu Abdullahi. Sparse signal recovery through a modified Dai-Yuan algorithm[J]. AIMS Mathematics, 2025, 10(8): 19675-19692. doi: 10.3934/math.2025877

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Abstract

Sparse signal recovery is a concept that is not only central to compressed sensing problems, but also apparent in magnetic resonance imaging (MRI) problems, machine learning, as well as statistical inference. In each of these fields, the target is finding sparse solutions to linear systems of equations that are underdetermined or ill-conditioned. In this paper, an efficient modified Dai-Yuan conjugate gradient method that is globally convergent irrespective of the line search procedure employed was developed to reconstruct sparse signals in compressed sensing. Results of the experiments conducted show that the method is promising.

References

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