Related papers: Homotopy Perturbation Method for Image Restoration…
Deep learning-based methods for low-light image enhancement typically require enormous paired training data, which are impractical to capture in real-world scenarios. Recently, unsupervised approaches have been explored to eliminate the…
In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
We show that the two couple equations derived by approximate symmetry method and approximate homotopy symmetry method are connected by a transformation for the perturbed PDEs. Consequently, approximate homotopy series solutions can be…
Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
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…
$ \ell_1 $-regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter $ t \in \mathbb{R}_{\geq 0} $ is a delicate issue. Instead of…
We analyze a recent application of homotopy perturbation method to some heat-like and wave-like models and show that its main results are merely the Taylor expansions of exponential and hyperbolic functions. Besides, the authors require…
In this paper, Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solutions for nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's…
We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are…
The induction motor behaviour is represented by a fifth order differential equation model. Addition of a torque correction factor to the model accurately reproduces the transient torques and instantaneous real and reactive power flows of…
In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms.…
This paper presents an improved and modified partial differential equation (PDE)-based de-hazing algorithm. The proposed method combines logarithmic image processing models in a PDE formulation refined with linear filter-based operators in…
Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The results heavily rely on the choice of appropriate functional…
Previous harmonization methods focus on adjusting one inharmonious region in an image based on an input mask. They may face problems when dealing with different perturbations on different semantic regions without available input masks. To…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the…
Blind image deblurring is a long standing challenging problem in image processing and low-level vision. Recently, sophisticated priors such as dark channel prior, extreme channel prior, and local maximum gradient prior, have shown promising…