Some class of parabolic systems applied to image processing

Abstract

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 Guo and al. ([19],[20]). 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.

An Efficient Algorithm for Reconstruction Images Corrupted by Some Multiplicative Noises

“…Image denoising is a substantial image processing task, the purpose of an image denoising algorithm is to achieve both noise reduction and feature preservation. Traditionally, additive gaussian noise is the most used to corrupt images and several methods and techniques have been used to reduce noise, see for instance [1,2,4,16,18,19,20,21,24,28] and for other approaches in image denoising see for instance [10,12]. In this case, for a given original corrupted image f , the problem is then to recover u from the data, which can be written as…”

“…It is well known that Total Variation (TV) can handle edges, but the images resulting from its application are usually piecewise constant, and have sometimes undesirable staircasing effect see for instance (cf. [2,4,6,7,13]), which causes images to look blocky. To overcome this, many regularization approaches (cf.…”

“…Using a MAP estimator, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. The energies studied here are inspired by image restoration with non linear variable exponent [1,2], and it is a combination of fast growth with respect to low gradient and slow growth when the gradient is large. We study a mathematical framework to prove the well posedness of the minimizer problem and we introduce the associated evolution problem, for which we derive numerical approaches.…”

A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration

“…To improve computational efficiency, we discretize (3) by (6) and we use the additive operator splitting scheme in the numerical implementation. On the other hand, the subdifferential Eq.…”

“…The aim is to remove noise while preserving edges, boundaries, and textures. To handle this problem, partial differential equations [1][2][3][4][5][6][7], variational models [8][9][10][11], energy minimization, bilateral filtering [12,13], and wavelet thresholding [14,15] have been proposed depending on the domain of applications. Generally, the partial differential equations use a nonlinear anisotropic diffusion to restore a degraded image which they seek to improve its quality by removing noise while preserving details and even enhancing edges.…”