相关论文: A $\ell_2-\ell_p$ regulariser based model for Pois…

We propose a nonlinear filter for noise removal based on the Laplacian for 1D and 2D data. The method utilizes the solution to a fourth-order nonlinear PDE involving the Laplacian for data reconstruction. Evolution equations are introduced…

A new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme is proposed in this paper, by embedding a recently introduced adaptive denoiser using the Schroedinger equation's solutions of quantum physics. The potential of…

It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…

This paper introduces a new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme based on a recently proposed denoiser using the Schroedinger equation's solutions of quantum physics. The efficiency of the proposed…

Phaseless diffraction measurements recorded by a CCD detector are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity to denoise Poisson phaseless measurement. The model…

$L_p$-norm regularization schemes such as $L_0$, $L_1$, and $L_2$-norm regularization and $L_p$-norm-based regularization techniques such as weight decay, LASSO, and elastic net compute a quantity which depends on model weights considered…

Digital sensors can lead to noisy results under many circumstances. To be able to remove the undesired noise from images, proper noise modeling and an accurate noise parameter estimation is crucial. In this project, we use a…

We present a simple discretization by radial basis functions for the Poisson equation with Dirichlet boundary condition. A Lagrangian multiplier using piecewise polynomials is used to accommodate the boundary condition. This simplifies…

This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…

Regularized optimization has been a classical approach to solving imaging inverse problems, where the regularization term enforces desirable properties of the unknown image. Recently, the integration of flow matching generative models into…

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations…

We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2)…

Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling…

A new image denoising algorithm to deal with the Poisson noise model is given, which is based on the idea of Non-Local Mean. By using the "Oracle" concept, we establish a theorem to show that the Non-Local Means Filter can effectively deal…

The reconstruction of low-rank matrix from its noisy observation finds its usage in many applications. It can be reformulated into a constrained nuclear norm minimization problem, where the bound $\eta$ of the constraint is explicitly given…

Hyperspectral images~(HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multi-scale low-rank tensor regularized $\ell_{2,p}$ (MLTL2p) approach for HSI…

It is known that the minimum-mean-squared-error (MMSE) denoiser under Gaussian noise can be written as a proximal operator, which suffices for asymptotic convergence of plug-and-play (PnP) methods but does not reveal the structure of the…

We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The $\ell_p$ norm covers a wide range of choices for the…

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…