Enhanced and restored signals as a generalized solution for shock filter models. Part II—numerical study |
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Authors: | M. Cheriet L. Remaki |
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Affiliation: | Imagery, Vision and Artificial Intelligence Laboratory, École de Technologie Supérieure, 1100 Notre-Dame West, Montreal, PQ H3C 1K3, Canada |
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Abstract: | In Part I of this paper, we proposed a well-posed generalized model for signal enhancement and restoration based on shock filters. A theoretical study of the Cauchy problem in the framework of generalized functions algebra was developed in detail. In Part II, we investigate the numerical aspects of the model. We derive an efficient, explicit numerical scheme in both one and two dimensions, and investigate the schemes' stability and convergence. Through experimental tests, we demonstrate the effectiveness of the numerical schemes when restoring and enhancing signals in various situations with a limited number of iterations. Moreover, we show the impact of the coefficients introduced in the model on the procedure's processing time. |
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Keywords: | Generalized functions Numerical schemes Signal enhancement and restoration Partial differential equations (PDEs) Shock filters |
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