相关论文: Solving Inverse Problems by Joint Posterior Maximi…

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Maximum-a-posteriori (MAP) estimation is the main Bayesian estimation methodology in imaging sciences, where high dimensionality is often addressed by using Bayesian models that are log-concave and whose posterior mode can be computed…

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…

We study a new family of inverse problems for recovering representations of corrupted data. We assume access to a pre-trained representation learning network R(x) that operates on clean images, like CLIP. The problem is to recover the…

Almost all existing methods for image restoration are based on optimizing the mean squared error (MSE), even though it is known that the best estimate in terms of MSE may yield a highly atypical image due to the fact that there are many…

In ill-posed imaging inverse problems, there can exist many hypotheses that fit both the observed measurements and prior knowledge of the true image. Rather than returning just one hypothesis of that image, posterior samplers aim to explore…

In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…

Intrinsic Image Decomposition (IID) is a challenging inverse problem that seeks to decompose a natural image into its underlying intrinsic components such as albedo and shading. While recent image decomposition methods rely on…

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…

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…

We propose a structured prior for high-dimensional Bayesian inverse problems based on a disentangled deep generative model whose latent space is partitioned into auxiliary variables aligned with known and interpretable physical parameters…

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…

A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…

This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form $f+h$ where $f$ is…

Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors.…

We consider the downlink of a cell-free massive multiple-input multiple-output (MIMO) system where large number of access points (APs) simultaneously serve a group of users. Two fundamental problems are of interest, namely (i) to maximize…

In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…