Image denoising by nonlinear nonlocal diffusion equations. (English) Zbl 1465.35385
Summary: In this paper, we propose and study a nonlinear nonlocal diffusion equation of the Perona-Malik type for the removal of Gaussian noise in images. Based on the fixed-point theorem, we prove the unique solvability of the equation. We also show that solutions of the nonlocal equation converge to the solution of the local spatially regularized Perona-Malik equation if the kernel is rescaled appropriately. The new equation inherits the merit of the nonlocal method that restores details and textures of noisy images but avoids speckles and artifacts in homogeneous regions. Comparisons with other nonlocal methods for image denoising are presented.
MSC:
| 35R09 | Integro-partial differential equations |
| 35K59 | Quasilinear parabolic equations |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
Perona-Malik equation; scale-space; removal of Gaussian noise in images; fixed-point theoremReferences:
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