A new nonlocal model for the restoration of textured images. (English) Zbl 1476.94010
Summary: In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of \(H^{-1}\) norm suggested by Y. Meyer [Oscillating patterns in image processing and nonlinear evolution equations. The fifteenth Dean Jacqueline B. Lewis memorial lectures. Providence, RI: American Mathematical Society (AMS) (2001; Zbl 0987.35003)] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer’s fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 45G10 | Other nonlinear integral equations |
| 47H10 | Fixed-point theorems |
| 68U10 | Computing methodologies for image processing |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
Keywords:
image denoising; nonlocal model; Schaeffer’s fixed-point theorem; textured images; nonlocal \(p\)-LaplacianCitations:
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