On a cross-diffusion system arising in image denoising
| Autor: | Gonzalo Galiano, Julián Velasco |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Generalization
Cross diffusion Noise reduction media_common.quotation_subject 010102 general mathematics Fidelity State (functional analysis) 01 natural sciences Signal 010101 applied mathematics Computational Mathematics Nonlinear system Computational Theory and Mathematics Computer Science::Computer Vision and Pattern Recognition Modeling and Simulation Applied mathematics 0101 mathematics Image denoising Mathematics media_common |
| Zdroj: | Computers & Mathematics with Applications. 76:984-996 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2018.05.035 |
| Popis: | We study a generalization of a cross-diffusion problem deduced from a nonlinear complex-variable diffusion model for signal and image denoising. We prove the existence of weak solutions of the time-independent problem with fidelity terms under mild conditions on the data problem. Then, we show that this translates on the well-posedness of a quasi-steady state approximation of the evolution problem, and also prove the existence of weak solutions of the latter under more restrictive hypothesis. We finally perform some numerical simulations for image denoising, comparing the performance of the cross-diffusion model to other well-known denoising methods. |
| Databáze: | OpenAIRE |
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