Related papers: Exploiting Prior Information in Block Sparse Signa…
Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted…
We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…
This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse…
Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…
This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…
A sparse recovery approach for direction finding in partly calibrated arrays composed of subarrays with unknown displacements is introduced. The proposed method is based on mixed nuclear norm and 1 norm minimization and exploits…
The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to…
Compressed Sensing (CS) is a signal processing technique which can accurately recover sparse signals from linear measurements with far fewer number of measurements than those required by the classical Shannon-Nyquist theorem. Block sparse…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error…