Related papers: A Stable Iterative Direct Sampling Method for Elli…
This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of bandlimited functions from folded samples and show that, for…
We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
Depth maps captured by modern depth cameras such as Kinect and Time-of-Flight (ToF) are usually contaminated by missing data, noises and suffer from being of low resolution. In this paper, we present a robust method for high-quality…
Low-rank matrix completion is a widely studied problem with many variants. Inductive matrix completion (IMC) incorporates row and column side information to significantly narrow the search space. Prior work falls into two regimes: methods…
In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form \[ \frac{\partial^{2}}{\partial…