Related papers: A signal recovery algorithm for sparse matrix base…
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…
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…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
In phase-only compressive sensing (PO-CS), our goal is to recover low-complexity signals (e.g., sparse signals, low-rank matrices) from the phase of complex linear measurements. While perfect recovery of signal direction in PO-CS was…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
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…
Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
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…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…