Related papers: Variational Iteration Method for Image Restoration
The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called Homotopy…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
This work concerns the Perona-Malik equation, which plays essential role in image processing. The first part gives a survey of results on existance, uniqueness and stability of solutions, the second part introduces discretisations of…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
In this paper we investigate convergence for the Variational Iteration Method (VIM) which was introduced and described in \cite{He0},\cite{He1}, \cite{He2}, and \cite{He3}. We prove the convergence of the iteration scheme for a linear…
Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…
Models including two $L^1$ -norm terms have been widely used in image restoration. In this paper we first propose the alternating direction method of multipliers (ADMM) to solve this class of models. Based on ADMM, we then propose the…
This paper investigates a novel class of regularizations of the Perona-Malik equation with variable exponents, of forward-backward parabolic type, which possess a variational structure and have potential applications in image processing.…
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
Many image restoration (IR) tasks require both pixel-level fidelity and high-level semantic understanding to recover realistic photos with fine-grained details. However, previous approaches often struggle to effectively leverage both the…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
Masked Image Modeling (MIM) has achieved impressive representative performance with the aim of reconstructing randomly masked images. Despite the empirical success, most previous works have neglected the important fact that it is…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We present a novel variational approach to image restoration (e.g., denoising, inpainting, labeling) that enables to complement established variational approaches with a histogram-based prior enforcing closeness of the solution to some…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
We propose a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…
When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…