A three-term Polak-Ribière-Polyak derivative-free method and its application to image restoration

Ibrahim, Abdulkarim Hassan; Deepho, Jitsupa; Abubakar, Auwal Bala; Adamu, Abubakar

doi:10.1016/j.sciaf.2021.e00880

Cited by 11 publications

(11 citation statements)

References 39 publications

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“…The SDYCG algorithm will be used to address this problem. Similar methods have been employed to deal with this problem; see [34][35][36]. All codes in this work are written in Matlab R2014a and run on an HP core i5, 8th Gen personal computer.…”

Section: Application In Signal Recoverymentioning

confidence: 99%

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

et al. 2022

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In this paper, we propose two scaled Dai–Yuan (DY) directions for solving constrained monotone nonlinear systems. The proposed directions satisfy the sufficient descent condition independent of the line search strategy. We also reasonably proposed two different relations for computing the scaling parameter at every iteration. The first relation is proposed by approaching the quasi-Newton direction, and the second one is by taking the advantage of the popular Barzilai–Borwein strategy. Moreover, we propose a robust projection-based algorithm for solving constrained monotone nonlinear equations with applications in signal restoration problems and reconstructing the blurred images. The global convergence of this algorithm is also provided, using some mild assumptions. Finally, a comprehensive numerical comparison with the relevant algorithms shows that the proposed algorithm is efficient.

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Section: Application In Signal Recoverymentioning

confidence: 99%

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

et al. 2022

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“…where b ∈  m is an observed signal, v 0 ∈  n is the unknown signal, 𝜔 is the noise and A ∈  m×n (m ≪ n) is a linear operator. In order to address problem (33), one of the tools usually employed is the 𝓁 1 -regularization. The restoration is obtained by solving the famous machine learning problem: the LASSO problem, that is,…”

Section: Application To Signal Recoverymentioning

confidence: 99%

“…The m × n matrix A is obtained by first filling it with independent samples of a standard Gaussian distribution and then ortho-normalizing the rows. The observation b is generated by (33), where 𝜔 is the Gaussian noise distributed as N(0, 𝛿 2 I) and 𝛿 ≥ 0 is the standard deviation (SD). We set 𝜇 = 0.01||A ⊤ b|| ∞ .…”

Section: Application To Signal Recoverymentioning

confidence: 99%

“…More precisely, the CG method has been paid attention to as an effective numerical method for solving large‐scale unconstrained optimization problems because of its simplicity and low storage 7,8 . Thus, using the projection technique in Solodov and Svaiter, 9 several researchers extended these methods resulting in derivative‐free methods (see References 10‐33 and references therein). Recently, based on Hestenes–Stiefel (HS) CG method 34 for unconstrained optimization, Wang et al 35 proposed a self‐adaptive three‐term derivative‐free method for solving monotone nonlinear equations with convex constraints.…”

Section: Introductionmentioning

confidence: 99%

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Accelerated derivative‐free method for nonlinear monotone equations with an application

Ibrahim

Abubakar

Adamu

2021

Numerical Linear Algebra App

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In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three‐term derivative‐free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133‐145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.

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“…Exploiting the simplicity and low storage requirement of the conjugate gradient method [1,2], in recent times, several authors have extended many conjugate gradient algorithms designed to solve unconstrained optimization problems to solve large-scale nonlinear equations (1.6) (see [3][4][5][6][7][8][9][10][11][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]36]). For instance, using the projection scheme of Solodov and Svaiter [35], Xiao and Zhu [38] extended the Hager and Zhang conjugate descent (CG DESCENT) method to solve (1.6).…”

Section: Introductionmentioning

confidence: 99%

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

Ibrahim¹,

ABUBAKAR²,

ABUBAKAR³

2022

CJM

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"Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images."

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A three-term Polak-Ribière-Polyak derivative-free method and its application to image restoration

Cited by 11 publications

References 39 publications

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

Accelerated derivative‐free method for nonlinear monotone equations with an application

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

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