Some class of parabolic systems applied to image processing. (English) Zbl 1352.35214
Summary: In this paper, we are interested in the mathematical and numerical study of a variational model derived as Reaction-Diffusion System for image denoising. We use a nonlinear regularization of total variation (TV) operator’s, combined with a decomposition approach of \(H^{-1}\) norm suggested by Z. Guo et al. [Nonlinear Anal., Real World Appl. 12, No. 5, 2904–2918 (2011; Zbl 1219.35340); Math. Comput. Modelling 53, No. 5–6, 1336–1350 (2011; Zbl 1217.65172)]. Based on Galerkin’s method, we prove the existence and uniqueness of the solution on Orlicz space for the proposed model. At last, compared experimental results distinctly demonstrate the superiority of our model, in term of removing noise while preserving the edges and reducing staircase effect.
MSC:
| 35Q94 | PDEs in connection with information and communication |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 35K57 | Reaction-diffusion equations |
Keywords:
image denoising; reaction-diffusion system; Orlicz space; Galerkin method; staircase effectReferences:
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