Related papers: Robust Estimation of Structural Orientation Parame…
The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…
Reliable localization is critical for robot navigation in complex indoor environments. In this paper, we propose an uncertainty-aware localization method that enhances the reliability of localization outputs without modifying the prediction…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open. We establish a small noise analysis framework to assess the…
In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction,…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
We study an ill-posed problem of geological field reconstruction under limited observations. Engineers often have to deal with the problem of reconstructing the subsurface geological field from sparse measurements such as exploration well…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
This work presents a systematic investigation into how alternative LiDAR-to-image projections affect metric place recognition when coupled with a state-of-the-art vision foundation model. We introduce a modular retrieval pipeline that…
Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the…
Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…