Related papers: Ocean Reverberation Suppression via Matrix Complet…
The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
Wireless sensor networks are widely adopted in military, civilian and commercial applications, which fuels an exponential explosion of sensory data. However, a major challenge to deploy effective sensing systems is the presence of {\em…
It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
In many autonomous mapping tasks, the maps cannot be accurately constructed due to various reasons such as sparse, noisy, and partial sensor measurements. We propose a novel map prediction method built upon the recent success of Low-Rank…
Matrix sensing has many real-world applications in science and engineering, such as system control, distance embedding, and computer vision. The goal of matrix sensing is to recover a matrix $A_\star \in \mathbb{R}^{n \times n}$, based on a…
Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
We consider the problem of high-dimensional channel estimation in fast time-varying millimeter-wave MIMO systems with a hybrid architecture. By exploiting the low-rank and sparsity properties of the channel matrix, we propose a two-phase…
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a…
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…