Related papers: Stable recovery guarantees for blind deconvolution…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key…
We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution $\mu$, from a binned Poisson convolution model. This question is motivated, among others, by super-resolution laser microscopy…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We adress the problem of Laplace deconvolution with random noise in a regression framework. The time set is not considered to be fixed, but grows with the number of observation points. Moreover, the convolution kernel is unknown, and…
This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the…
In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted…
We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel's measurements are given as convolution of a common source signal and sparse…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Modulo sampling enables acquisition of signals with unlimited dynamic range by folding the input into a bounded interval prior to sampling, thus eliminating the risk of signal clipping and preserving information without requiring…
Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD does not admit a unique solution. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and…
Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point…
Super-resolution and denoising are ill-posed yet fundamental image restoration tasks. In blind settings, the degradation kernel or the noise level are unknown. This makes restoration even more challenging, notably for learning-based…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…