Related papers: MAP Estimation with Denoisers: Convergence Rates a…
Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the…
This paper presents a new convergent Plug-and-Play (PnP) algorithm. PnP methods are efficient iterative algorithms for solving image inverse problems formulated as the minimization of the sum of a data-fidelity term and a regularization…
Prior probability models are a fundamental component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided…
A common approach to solve inverse imaging problems relies on finding a maximum a posteriori (MAP) estimate of the original unknown image, by solving a minimization problem. In thiscontext, iterative proximal algorithms are widely used,…
Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…
In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex…
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…
In this paper we analyze the Gradient-Step Denoiser and its usage in Plug-and-Play algorithms. The Plug-and-Play paradigm of optimization algorithms uses off the shelf denoisers to replace a proximity operator or a gradient descent operator…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…
This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…