Related papers: A $\ell_2-\ell_p$ regulariser based model for Pois…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
We consider the unconstrained $L_2$-$L_p$ minimization: find a minimizer of $\|Ax-b\|^2_2+\lambda \|x\|^p_p$ for given $A \in R^{m\times n}$, $b\in R^m$ and parameters $\lambda>0$, $p\in [0,1)$. This problem has been studied extensively in…
Imaging polarimetry allows more information to be extracted from a scene than conventional intensity or colour imaging. However, a major challenge of imaging polarimetry is image degradation due to noise. This paper investigates the…
We consider the challenging blind denoising problem for Poisson-Gaussian noise, in which no additional information about clean images or noise level parameters is available. Particularly, when only "single" noisy images are available for…
We extend the blindspot model for self-supervised denoising to handle Poisson-Gaussian noise and introduce an improved training scheme that avoids hyperparameters and adapts the denoiser to the test data. Self-supervised models for…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
Several approaches are discussed how to understand the solution of the Dirichlet problem for the Poisson equation when the Dirichlet data are non-smooth such as if they are in $L^2$ only. For the method of transposition (sometimes called…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called…
Despite recent advances, developing general-purpose universal denoising and artifact-removal networks remains largely an open problem: Given fixed network weights, one inherently trades-off specialization at one task (e.g.,~removing Poisson…
Plug-and-Play Priors (PnP) is a popular framework for solving imaging inverse problems by integrating learned priors in the form of denoisers trained to remove Gaussian noise from images. In standard PnP methods, the denoiser is applied…
We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…
The 3D block matching (BM3D) filter belongs to the state-of-the-art techniques for eliminating additive white Gaussian noise from single-frame images. There exist four multi-frame extensions of BM3D as of today. In this work, we combine…
Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
Plug-and-play (PnP) denoising is a popular iterative framework for solving imaging inverse problems using off-the-shelf image denoisers. Their empirical success has motivated a line of research that seeks to understand the convergence of…
In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable…
In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting…
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…
Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…