A Second-Order Continuous-Time Dynamical System for Solving Sparse Image Restoration Problems

Wenjie Wang (), Chunyan Wang and Mengzhen Li
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Wenjie Wang: School of Management Science, Qufu Normal University, Rizhao 276800, China
Chunyan Wang: School of Management Science, Qufu Normal University, Rizhao 276800, China
Mengzhen Li: School of Management Science, Qufu Normal University, Rizhao 276800, China

Mathematics, 2024, vol. 12, issue 15, 1-15

Abstract: The quality of images captured digitally or transmitted over networks is distorted by noise during the process. The current methods of image restoration can be ineffective in dealing with intricate noise patterns or may be slow or imprecise. This paper fills this gap by presenting a new second-order continuous-time dynamical system for denoising of images in image restoration. The approach used in this work poses the problem as a convex quadratic program that can, thus, be solved for optimality. The existence and uniqueness of a global solution are theoretically demonstrated, and the condition for the global strong convergence of the system’s trajectory is provided. The method presented in this paper is shown to be useful in a number of experiments on image restoration. As for the performance, it is higher than that of other known algorithms, with an average SNR equal to 34.78 and a Structural Similarity Index Measure (SSIM) of 0.959 for the reconstructed images. Such improvements demonstrate the effectiveness of the second-order dynamical system approach in actual image restoration applications.

Keywords: dynamicalsystem; image restoration; noise reduction; image processing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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