Related papers: Back-Projection based Fidelity Term for Ill-Posed …

Accurate reconstruction of computed tomography (CT) images is crucial in medical imaging field. However, there are unavoidable interpolation errors in the backprojection step of the conventional reconstruction methods, i.e.,…

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used…

In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. Construction of an adaptive optimal solution for such problems usually relies either on a singular value…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Deep Equilibrium Models (DEQs) are implicit neural networks with fixed points, which have recently gained attention for learning image regularization functionals, particularly in settings involving Gaussian fidelities, where assumptions on…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and…

This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…

Inverse reinforcement learning (IRL) for linear systems seeks a cost function whose optimal controller reproduces an expert policy from data. Existing data-driven methods for discrete-time linear systems are largely built on iterative…

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…

The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…

Variational models for image deblurring problems typically consist of a smooth term and a potentially non-smooth convex term. A common approach to solving these problems is using proximal gradient methods. To accelerate the convergence of…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

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…

During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a…

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…