Related papers: Solving Inverse Problems by Joint Posterior Maximi…

Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned…

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…

We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative…

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…

We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…

This paper presents a novel methodology for solving the time-optimal trajectory optimization problem for interplanetary solar-sail missions using successive convex programming. Based on the non-convex problem, different convexification…

A significant number of researchers have applied deep learning methods to image fusion. However, most works require a large amount of training data or depend on pre-trained models or frameworks to capture features from source images. This…

Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are…

This paper aims to study a majorized alternating direction method of multipliers with indefinite proximal terms (iPADMM) for convex composite optimization problems. We show that the majorized iPADMM for 2-block convex optimization problems…

This paper discusses the computational resolution and presents numerical results for solving affine combinations of Heaviside composite optimization problems (abbreviated as A-HSCOPs) by a progressive integer programming (abbreviated as…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…

The analytical deep image prior (ADP) introduced by Dittmer et al. (2020) establishes a link between deep image priors and classical regularization theory via bilevel optimization. While this is an elegant construction, it involves…

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources.…

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…