Related papers: Solving Implicit Inverse Problems with Homotopy-Ba…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
In this paper, we propose algorithms that exploit negative curvature for solving noisy nonlinear nonconvex unconstrained optimization problems. We consider both deterministic and stochastic inexact settings, and develop two-step algorithms…
In this paper, we discuss the construction, analysis and implementation of a novel iterative regularization scheme with general convex penalty term for nonlinear inverse problems in Banach spaces based on the homotopy perturbation…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…
Over the past decade, stochastic algorithms have emerged as scalable and efficient tools for solving large-scale ill-posed inverse problems by randomly selecting subsets of equations at each iteration. However, due to the ill-posedness and…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…
For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…
In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…
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…
Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…