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Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
For robust visual-inertial SLAM in perceptually-challenging indoor environments,recent studies exploit line features to extract descriptive information about scene structure to deal with the degeneracy of point features. But existing…
The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
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 tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…
Deep Neural Networks (DNNs) are well-known to act as over-parameterized deep image priors (DIP) that regularize various image inverse problems. Meanwhile, researchers also proposed extremely compact, under-parameterized image priors (e.g.,…
The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…
A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…
Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
Learning from expert demonstrations to flexibly program an autonomous system with complex behaviors or to predict an agent's behavior is a powerful tool, especially in collaborative control settings. A common method to solve this problem is…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
Functional autoregressive (FAR) models provide a fundamental framework for analyzing temporally dependent functional data. However, the infinite-dimensional nature of the underlying Hilbert space introduces intrinsic ill-posedness, as the…
The $\chi^2$ principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing…
Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…