Related papers: Generalized Expectation Consistent Signal Recovery…
In this paper, we propose an adaptive matched detector of a signal corrupted by a non-Gaussian noise with an inverse gamma texture. The detector is formed using a set of secondary data measurements, and is analytically shown to have a…
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of $m$ measurements, $y_k = |\mathbf a_k^* \mathbf x|$ for $k = 1, \dots, m$, is it possible to recover $\mathbf x \in \mathbb{C}^n$ (i.e., length-$n$…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
Conventional priors used for signal recovery are often limited by the assumption that the type of a signal's variability, such as piecewise constant or linear behavior, is known and fixed. This assumption is problematic for complex signals…
We consider the problem of recovering elements of a low-dimensional model from linear measurements. From signal and image processing to inverse problems in data science, this question has been at the center of many applications. Lately,…
In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…
Graph signals arise from physical networks, such as power and communication systems, or as a result of a convenient representation of data with complex structure, such as social networks. We consider the problem of general graph signal…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector ${\mathbf x}$ in ${\mathbb R}^d$ or ${\mathbb C}^d$ through quadratic samples ${\mathbf x}^*A_1{\mathbf x}, \dots, {\mathbf…
An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\cal X}$ from indirect observation $\omega=Ax+\xi$ of $x$ corrupted by random noise $\xi$ with finite covariance matrix.…
An algorithm for continuous time-delay estimation from sampled output data and known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm…