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This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…
We present a method to solve numerically the Cauchy problem for the defocusing nonlinear Schr\"{o}dinger (NLS) equation with a box-type initial condition (IC) having a nontrivial background of amplitude $q_o>0$ as $x\to \pm \infty$ by…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…
We consider the problem of recovering a real-valued $n$-dimensional signal from $m$ phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objective. We establish local convergence of subgradient descent…
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff…
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
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…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
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…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…