Related papers: LINPRO: linear inverse problem library for data co…
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Signal to noise ratio is key to any measurement. Recent progress in semi/super-conductor technology have pushed the signal detection sensitivity to the ultimate quantum level, but the noise issue remains largely untouched and, in many…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…
Classical Kullback-Leibler or entropic distances are known to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations the data available to a decision maker…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…
One of the greatest data analysis challenges for the Laser Interferometer Space Antenna (LISA) is the need to account for a large number of gravitational wave signals from compact binary systems expected to be present in the data. We…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…
In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
In this study, we introduce two new Krylov subspace methods for solving rectangular large-scale linear inverse problems. The first approach is a modification of the Hessenberg iterative algorithm that is based off an LU factorization and is…
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…