2026· Journal of Convex Analysis· 0 citations· 56 references
TL;DR
A discretisation based on a second-order consistent Grünwald Letnikov scheme is introduced and some numerical simulations aiming to denoise images corrupted by impulsive noise are shown, which can be well modeled by the Laplace distribution.
Abstract
We introduce and study a variational model for signal and image denoising based on Riemann-Liouville fractional derivatives of every positive order higher than zero. Both the one-dimensional and two-dimensional cases are studied. The model exploits an
L^1
L
1
fitting data term together with both right and left Riemann-Liouville fractional derivatives as regularizing terms, with the aim of achieving an orientation independent analysis. To provide evidence of effectiveness for the proposed model we introduce a discretisation based on a second-order consistent Grünwald Letnikov scheme and show some numerical simulations aiming to denoise images corrupted by impulsive noise, which can be well modeled by the Laplace distribution.
We study the inverse problem of identifying an unknown time-dependent source in a linear time-fractional diffusion equation, where the time derivative is taken in the Caputo sense of fractional order α . The problem is ill-posed in the sense of Hadamard: the solution does not depend continuously on the measured data, s...
Ouarda Tabrha, Naceur Rahmani, C. Latrous· Gulf Journal of Mathematics· 0 citations
We consider variational image denoising with spatially dependent Orlicz regularization and introduce an Orlicz--Sobolev approximation of the ROF model based on a scaled $L\log L$-type density. For a general class of uniformly superlinear integrands satisfying a $\Delta_2$-condition, we establish existence and uniquenes...
A novel nonlinear evolution model that integrates a Caputo time‐fractional derivative with a variable exponent diffusion operator for image decomposition and noise removal and preserves positivity, a key property for image processing applications is proposed.
Anouar Ben-loghfyry, Abderrahim Charkaoui· Mathematical methods in the...· 0 citations
Improved reconstruction performance can be achieved by the proposed model compared with classical TV, biharmonic, and TV2 inpainting methods, and is duly proved through quantitative assessments based on Peak Signal-to-Noise Ratio, Structural Similarity Index Measure, and Mean Squared Error.
Ahmed K. Al-Jaberi, A. Lupaș, D. Lupaş· Mathematical and Computation...· 0 citations
A new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation which allows only the decomposition of phase values into multiple layers.
Acar Ruyam· Balkan Journal of Electrical...· 0 citations
Abstract In this paper, we study an inverse random source problem for the fourth-order fractional diffusion equation, where the source is driven by fractional Brownian motion (fBm). For the direct problem, we establish regularity results for the solutions under specific conditions. For the inverse problem, we prove the...
Ao-Ran Bei, Hao Cheng· Journal of Inverse and Ill-P...· 0 citations
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