On some evolution equation with combined local and nonlocal \(p(x,[\nabla u])\)-Laplace operator for image denoising. (English) Zbl 1537.94017
Summary: Image denoising is an important topic in image processing. This paper proposes a novel approach to speckle noise removal using a combination of nonlocal and local variable \(p(x,[\nabla u])\)-exponents. The existence of a strong solution for the regularization problem is shown through Galerkin’s approximation. Furthermore, the denoising model is rigorously evaluated against various benchmark datasets, and performance metrics such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are computed. These statistical measures offer quantitative evidence of the chosen variable exponent parameter \(p(x,[\nabla u])\) denoising model’s superior performance compared to existing methods. The model demonstrates its efficacy in preserving image quality, reducing noise, and enhancing visual fidelity, thus validating the effectiveness of the chosen parameter.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 68U10 | Computing methodologies for image processing |
| 35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65K10 | Numerical optimization and variational techniques |
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