Related papers: Iterative algorithms for a non-linear inverse prob…
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
We present a new approach for statistical inference on noise properties of CMB anisotropy data. We consider a Maximum Likelihood parametric estimator to recover the full dependence structure of the noise process. We also consider a…
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each…
The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy of models with noisy parameters, we consider the problem of…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
Specular reflection can be problematic for the determination of the cloud thermodynamic phase for near-nadir-pointing space LIDARs. A LIDAR system biased towards the specular contribution for backscatter, if near-concurrent to a…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar…
We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…
LiDAR point clouds captured in rain or snow are often corrupted by weather-induced returns, which can degrade perception and safety-critical scene understanding. This paper proposes Intensity- and Distance-Aware Statistical Outlier Removal…
Computed Tomography is one of the efficient and vital modalities of non-destructive techniques (NDT). Various factors influence the CT reconstruction result, including limited projection data, detector electronics optimization, background…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…