Image restoration using a conjugate gradient-based adaptive filtering algorithm

Joo, Kyung Sub; Bose, T.; Xu, Guo Fang

doi:10.1007/bf01183274

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…As a means of easing the restoration work, there is a need to balance the amount of noise present in corrupted images which play an important role in determining the efficiency of any restoration algorithm. This area has recently gained a lot of attention because of its vast applications (see [19][20][21][22][23]). However, with recent advances in numerical methods, there is a need to explore more efficient algorithms capable of producing efficient results.…”

Section: Applicationmentioning

confidence: 99%

Generalized RMIL conjugate gradient method under the strong Wolfe line search with application in image processing

Awwal,

Wang,

Kumam

et al. 2023

Math Methods in App Sciences

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RMIL conjugate gradient method originally proposed by Rivaie et al. (2012) has recently gained lots of attention. In this article, we propose a generalized conjugate gradient parameter that contains both RMIL and its variant, that is, RMIL+, as special cases. We show that the search direction generated by the new method is sufficiently descent. Under standard mild conditions, we discuss the convergence analysis of the propose method. We demonstrate the numerical efficiency of the propose method on a set of unconstrained minimization benchmark test problems as well as an image restoration problem. The results of the experiment reveal that the proposed method performs better than its main competitors.

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Section: Applicationmentioning

confidence: 99%

Generalized RMIL conjugate gradient method under the strong Wolfe line search with application in image processing

Awwal,

Wang,

Kumam

et al. 2023

Math Methods in App Sciences

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“…Moreover, for the image restoration problem, some modified Hestenes-Stiefel conjugate gradient algorithms were presented by Hu et al (2020). Other CG algorithms (Cao and Wu, 2020;Joo et al, 1997), for this purpose, were also brought in the literature. In addition to them, some improved CG methods such as those of (Mtagulwa and Kaelo, 2019;Jiang and Jian, 2019;Wang et al, 2018;Fatemi, 2016) were presented for general optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Geometri Uydurma için En İyi Eşlenik Gradyan Yönteminin Tespit Edilmesi

Kiran

2022

Konya Journal of Engineering Sciences

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In this study, it is aimed to determine the optimal conjugate gradient (CG) method for the geometry fitting of 2D measured profiles. To this end, the three well-known CG methods such as the Fletcher-Reeves, Polak-Ribiere and Hestenes-Stiefel were employed. For testing those methods performances, the five primitive geometries accommodating circle, square, triangle, ellipse and rectangle were first built with a 3D printer, and then they were scanned with a coordinate measuring machine (CMM) to achieve their 2D profiles. The nonlinear least squares procedure was implemented to minimize the error between those measured data and modeled ones. An iterative line search was utilized for this task. The search direction was calculated using the above-mentioned CG methods. During the geometry fitting process, the number of function evaluations at each iteration were computed and the total number of function evaluations were set to be a performance measure of the CG method in question when it converged. By using these performance measures, the performance and data profiles were created to efficiently determine the optimal CG method. Based on performance profiles, it can be stated that the Fletcher-Reeves and Polak-Ribiere methods are the fastest ones on three test geometries out of five. In addition to that, all the CG methods were able to complete the geometry fitting of 80% of test geometries. On the other hand, by examining the data profiles, it was determined that the Polak-Ribiere and Hestenes-Stiefel methods achieve their maximum capabilities of the completing geometry fitting (i.e., 80%) with much lower number of function evaluations than the Fletcher-Reeves method. Besides, in most geometries, the Polak-Ribiere method outperformed the others, thereby it was determined to be the optimal one for the geometry fitting. As a conclusion, the reported results in this work might help the end-users who study on the CMM data processing to conduct an efficient geometry fitting.

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“…It has been shown that the stability and convergence performance of the CG algorithm are highly determined by the parameters α n and β n , as well as the data windowing schemes for autocorrelation matrix R and cross-correlation vector p. Recently, many modifications to the CG algorithm have been proposed [94,[97][98][99][100][101]. These modified CG algorithms are successfully applied into the adaptive equalizer, system identification, linear prediction and so on.…”

Section: Basic Cg Algorithmmentioning

confidence: 99%

“…It is observed when the termination condition is set to min(n, N, M ), the GDW-CGII algorithm results in better performance. We believe that the generalized data windowing scheme can also be extended to other type CG algorithms like the constrained CG algorithm [97] and the sample-based CG algorithm [101].…”

Section: Filteringmentioning

confidence: 99%

Performance analysis and enhancements of adaptive algorithms and their applications

Zhao¹

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Adaptive filters that self-adjust their transfer functions according to optimizing algorithms are powerful adaptive systems with numerous applications in the fields of signal processing, communications, radar, sonar, seismology, navigation systems and biomedical engineering. An adaptive signal processing algorithm, e.g., the least mean squares (LMS) algorithm and the recursive least square (RLS) algorithm, is used to deal with adaptation

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Image restoration using a conjugate gradient-based adaptive filtering algorithm

Cited by 9 publications

References 14 publications

Generalized RMIL conjugate gradient method under the strong Wolfe line search with application in image processing

Generalized RMIL conjugate gradient method under the strong Wolfe line search with application in image processing

Geometri Uydurma için En İyi Eşlenik Gradyan Yönteminin Tespit Edilmesi

Performance analysis and enhancements of adaptive algorithms and their applications

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