Related papers: On the Development of a Coupled Non-linear Telegra…
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
In this paper, we consider a new coupled PDE model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in…
Image restoration is rather challenging in adverse weather conditions, especially when multiple degradations occur simultaneously. Blind image decomposition was proposed to tackle this issue, however, its effectiveness heavily relies on the…
Color polarization demosaicking (CPDM) aims to reconstruct full-resolution polarization images of four directions from the color-polarization filter array (CPFA) raw image. Due to the challenge of predicting numerous missing pixels and the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean…
In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…
Restoring real-world degraded images, such as old photographs or low-resolution images, presents a significant challenge due to the complex, mixed degradations they exhibit, such as scratches, color fading, and noise. Recent data-driven…
The images produced by diffusion models can attain excellent perceptual quality. However, it is challenging for diffusion models to guarantee distortion, hence the integration of diffusion models and image compression models still needs…
This work proposes a novel method based on a pseudo-parabolic diffusion process to be employed for texture recognition. The proposed operator is applied over a range of time scales giving rise to a family of images transformed by nonlinear…
The transport of intensity equation (TIE) has revolutionized phase retrieval in optical microscopy, yet its application to complex media with absorption/scattering remains challenging. Here, we present a coupled TIE-TPE (transport of phase…
We present a novel iterative scheme for restoring uneven illumination in grayscale images. Our approach solves, at each global iteration, a nonlinear elliptic equation for an auxiliary field $u$ and then updates the illumination via an…
The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them,…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
In this work, we propose a multiscale approach for a nonstandard higher-order PDE based on the $p(\cdot)$-Kirchhoff energy. First, we consider a topological gradient approach for a semilinear case in order to detect important object of…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images is to combine the forward and backward diffusion equations. However, the latter problem is well known to be exponentially…
This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…