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The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
A novel compressive-sensing based signal multiplexing scheme is proposed in this paper to further improve the multiplexing gain for multiple input multiple output (MIMO) system. At the transmitter side, a Gaussian random measurement matrix…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…
Compressive sensing (CS) is a new approach for the acquisition and recovery of sparse signals and images that enables sampling rates significantly below the classical Nyquist rate. Despite significant progress in the theory and methods of…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix and then uses linear programming to decode information…
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…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
Compressive sensing (CS) technologies present many advantages over other existing approaches for implementing wideband spectrum sensing in cognitive radios (CRs), such as reduced sampling rate and computational complexity. However, there…
In this paper we develop a novel computational sensing framework for sensing and recovering structured signals. When trained on a set of representative signals, our framework learns to take undersampled measurements and recover signals from…
Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…
Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have…
We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…
Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via…
This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical…
In a structural health monitoring (SHM) system that uses digital cameras to monitor cracks of structural surfaces, techniques for reliable and effective data compression are essential to ensure a stable and energy efficient crack images…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…