Measurement design for detecting sparse signals

Zahedi, Ramin; Pezeshki, Ali; Chong, Edwin K. P.

doi:10.1016/j.phycom.2011.09.007

Cited by 18 publications

(29 citation statements)

References 30 publications

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“…Therefore, when designing rows of the measurement matrix, each measurement row a T k can be divided into two parts: the first part is a 16-dimensional vector with norm 1, and the second part is a 59-dimensional vector of zeros. Moreover, our actions are chosen from a static library of 50 measurement vectors that together, build a Grassmannian line packing (see [10] and [11]) in R 16 . We also assume that v ∼ N (0, σ 2 ).…”

Section: Simulation Resultsmentioning

confidence: 99%

Adaptive compressive sampling using partially observable markov decision processes

Zahedi

Krakow

Chong

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We present an approach to adaptive measurement selection in compressive sensing for estimating sparse signals. Given a fixed number of measurements, we consider the sequential selection of the rows of a compressive measurement matrix to maximize the mutual information between the measurements and the sparse signal's support. We formulate this problem as a partially observable Markov decision process (POMDP), which enables the application of principled reasoning for sequential measurement selection based on Bellman's optimality condition.

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Section: Simulation Resultsmentioning

confidence: 99%

Adaptive compressive sampling using partially observable markov decision processes

Zahedi

Krakow

Chong

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Theorem 1. The measurement sub-matrix Φ s in (9) is the solution to the following optimization problem…”

Section: A Maximally-uncorrelated Compressive Detectormentioning

confidence: 99%

“…October 9, 2018 DRAFT In other words, the rows of Φ s in (9) represent the set of M 1 uncorrelated measurement devices that maximize the expected value of total energy (or the total variance) in their outputs.…”

Section: A Maximally-uncorrelated Compressive Detectormentioning

confidence: 99%

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Compressive Detection of Random Subspace Signals

Razavi

Valkama

Čabrić

2016

IEEE Trans. Signal Process.

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The problem of compressive detection of random subspace signals is studied. We consider signals modeled as $\mathbf{s} = \mathbf{H} \mathbf{x}$ where $\mathbf{H}$ is an $N \times K$ matrix with $K \le N$ and $\mathbf{x} \sim \mathcal{N}(\mathbf{0}_{K,1},\sigma_x^2 \mathbf{I}_K)$. We say that signal $\mathbf{s}$ lies in or leans toward a subspace if the largest eigenvalue of $\mathbf{H} \mathbf{H}^T$ is strictly greater than its smallest eigenvalue. We first design a measurement matrix $\mathbf{\Phi}=[\mathbf{\Phi}_s^T,\mathbf{\Phi}_o^T]^T$ comprising of two sub-matrices $\mathbf{\Phi}_s$ and $\mathbf{\Phi}_o$ where $\mathbf{\Phi}_s$ projects the signals to the strongest left-singular vectors, i.e., the left-singular vectors corresponding to the largest singular values, of subspace matrix $\mathbf{H}$ and $\mathbf{\Phi}_o$ projects it to the weakest left-singular vectors. We then propose two detectors which work based on the difference in energies of the samples measured by two sub-matrices $\mathbf{\Phi}_s$ and $\mathbf{\Phi}_o$ and prove their optimality. Simplified versions of the proposed detectors for the case when the variance of noise is known are also provided. Furthermore, we study the performance of the detector when measurements are imprecise and show how imprecision can be compensated by employing more measurement devices. The problem is then re-formulated for the case when the signal lies in the union of a finite number of linear subspaces instead of a single linear subspace. Finally, we study the performance of the proposed methods by simulation examples.Comment: 33 pages, 11 figures, Revised versio

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“…Theories and concepts developed in CS for sparse signal recovery have been exploited in the recent literature for signal detection problems [8]- [23]. These works include deriving performance bounds for CS based signal detection [9], [10], [12], [13], [17], [18], [20], [21], [23], developing algorithms [8], [15], [16] and designing low dimensional projection matrices [14], [22]. While some of the work, such as [8], [9], [15], [16], [19]- [21] focused on sparse signal detection when the underlying subspace where the signal lies is unknown, some other works [12]- [14], [17], [18] considered the problem of detecting signals which are not necessarily sparse.…”

Section: Introductionmentioning

confidence: 99%

Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation

Wimalajeewa

Varshney

2017

IEEE Trans. on Signal and Inf. Process. over Networks

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Abstract-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 share a common but unknown support. While in the traditional compressive sensing (CS) framework, the goal is to recover the complete sparse signal, in sparse signal detection, complete signal recovery may not be necessary to make a reliable detection decision. In particular, detection can be performed based on partially or inaccurately estimated signals which requires less computational burden than that is required for complete signal recovery. To that end, we investigate the problem of sparse signal detection based on partially estimated support set. First, we discuss how to determine the minimum fraction of the support set to be known so that a desired detection performance is achieved in a centralized setting. Second, we develop two distributed algorithms for sparse signal detection when the raw compressed observations are not available at the central fusion center. In these algorithms, the final decision statistic is computed based on locally estimated partial support sets via orthogonal matching pursuit (OMP) at individual nodes. The proposed distributed algorithms with less communication overhead are shown to provide comparable performance (sometimes better) to the centralized approach when the size of the estimated partial support set is very small. Index Terms-Compressive sensing, sparse signal detection, partial support set estimation, orthogonal matching pursuit (OMP)

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Measurement design for detecting sparse signals

Cited by 18 publications

References 30 publications

Adaptive compressive sampling using partially observable markov decision processes

Adaptive compressive sampling using partially observable markov decision processes

Compressive Detection of Random Subspace Signals

Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation

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