Compressed sensing with sequential observations

Malioutov, Dmitry; Sanghavi, Sujay; Willsky, A. S.

doi:10.1109/icassp.2008.4518370

Cited by 44 publications

(34 citation statements)

References 5 publications

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“…Further, authors in [52] studied a two-step CS scheme with the aim of minimizing the sampling rate, where the actual sparsity was estimated in the first time slot and the compressed measurements were then adjusted in the second slot. In [110], a sequential CS approach has been proposed where each compressed measurement was acquired in sequence. In this sequential CS approach, observations become available sequentially and the process can be stopped as soon as there is a reasonable certainty of correct reconstruction.…”

Section: Wideband Spectrum Sensingmentioning

confidence: 99%

Application of Compressive Sensing in Cognitive Radio Communications: A Survey

Sharma

Lagunas

Chatzinotas

et al. 2016

IEEE Commun. Surv. Tutorials

210

112

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Abstract-Compressive Sensing (CS) has received much attention in several fields such as digital image processing, wireless channel estimation, radar imaging, and Cognitive Radio (CR) communications. Out of these areas, this survey paper focuses on the application of CS in CR communications. Due to the underutilization of the allocated radio spectrum, spectrum occupancy is usually sparse in different domains such as time, frequency and space. Such a sparse nature of the spectrum occupancy has inspired the application of CS in CR communications. In this regard, several researchers have already applied the CS theory in various settings considering the sparsity in different domains. In this direction, this survey paper provides a detailed review of the state of the art related to the application of CS in CR communications. Starting with the basic principles and the main features of CS, it provides a classification of the main usage areas based on the radio parameter to be acquired by a wideband CR. Subsequently, we review the existing CSrelated works applied to different categories such as wideband sensing, signal parameter estimation and Radio Environment Map (REM) construction, highlighting the main benefits and the related issues. Furthermore, we present a generalized framework for constructing the REM in compressive settings. Finally, we conclude this survey paper with some suggested open research challenges and future directions.

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Section: Wideband Spectrum Sensingmentioning

confidence: 99%

Application of Compressive Sensing in Cognitive Radio Communications: A Survey

Sharma

Lagunas

Chatzinotas

et al. 2016

IEEE Commun. Surv. Tutorials

210

112

View full text Add to dashboard Cite

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“…The sparse nonzero support is chosen as in (4), and the amplitudes of the nonzero elements are Gaussian distributed as in (6). The AIC sampler is used and the LASSO algorithm is employed for sparse signal recovery in the presence of ambient noise.…”

Section: Performance Evaluationsmentioning

confidence: 99%

“…Thus, the practical sampling rate has to be set conservatively based on S max in lieu of S nz , which may result in an unnecessarily high sampling rate as S max deviates from S nz . A remedy to this wastage of the sampling resources is by adopting sequential sampling techniques [4], [5]. In [4], one sample is taken at a time, and the sparse signal is recovered at each time based on batch processing of all the past samples.…”

Section: Introductionmentioning

confidence: 99%

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Sparsity Order Estimation and its Application in Compressive Spectrum Sensing for Cognitive Radios

Wang

Tian

Feng

2012

IEEE Trans. Wireless Commun.

128

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Abstract-Compressive sampling techniques can effectively reduce the acquisition costs of high-dimensional signals by utilizing the fact that typical signals of interest are often sparse in a certain domain. For compressive samplers, the number of samples Mr needed to reconstruct a sparse signal is determined by the actual sparsity order Snz of the signal, which can be much smaller than the signal dimension N . However, Snz is often unknown or dynamically varying in practice, and the practical sampling rate has to be chosen conservatively according to an upper bound Smax of the actual sparsity order in lieu of Snz, which can be unnecessarily high. To circumvent such wastage of the sampling resources, this paper introduces the concept of sparsity order estimation, which aims to accurately acquire Snz prior to sparse signal recovery, by using a very small number of samples Me less than Mr. A statistical learning methodology is used to quantify the gap between Mr and Me in a closed form via data fitting, which offers useful design guideline for compressive samplers. It is shown that Me ≥ 1.2Snz log(N/Snz + 2) + 3 for a broad range of sampling matrices. Capitalizing on this gap, this paper also develops a two-step compressive spectrum sensing algorithm for wideband cognitive radios as an illustrative application. The first step quickly estimates the actual sparsity order of the wide spectrum of interest using a small number of samples, and the second step adjusts the total number of collected samples according to the estimated signal sparsity order. By doing so, the overall sampling cost can be minimized adaptively, without degrading the sensing performance.

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“…This includes (i) homotopy methods, e.g. [55], [56], whose goal is to only speed up the optimization algorithm using homotopy or warm starts and the previous reconstructed signal, but not to reduce the number of measurements required; (ii) [57], [55], [58], [59] which reconstruct a single signal from sequentially arriving measurements; and (iii) [60], [61], [62], which iteratively improve support estimation for a single sparse signal. Another recent work [63] proposes causal but batch methods.…”

Section: B Related Workmentioning

confidence: 99%

Recursive Reconstruction of Sparse Signal Sequences

Vaswani

2013

Compressed Sensing &Amp; Sparse Filtering

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In this chapter, we describe our recent work on the design and analysis of recursive algorithms for causally reconstructing a time sequence of (approximately) sparse signals from a greatly reduced number of linear projection measurements. The signals are sparse in some transform domain referred to as the sparsity basis and their sparsity patterns (support set of the sparsity basis coefficients) can change with time. By "recursive", we mean use only the previous signal's estimate and the current measurements to get the current signal's estimate. We also briefly summarize our exact reconstruction results for the noise-free case and our error bounds and error stability results (conditions under which a time-invariant and small bound on the reconstruction error holds at all times) for the noisy case. Connections with related work are also discussed.A key example application where the above problem occurs is dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology and MRI-guided surgery, or in functional MRI to track brain activation changes. Cross-sectional images of the brain, heart, larynx or other human organ images are piecewise smooth, and thus approximately sparse in the wavelet domain. In a time sequence, their sparsity pattern changes with time, but quite slowly. The same is also often true for the nonzero signal values. This simple fact, which was first observed in our work, is the key reason that our proposed recursive algorithms can achieve provably exact or accurate reconstruction from very few measurements.

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Compressed sensing with sequential observations

Cited by 44 publications

References 5 publications

Application of Compressive Sensing in Cognitive Radio Communications: A Survey

Application of Compressive Sensing in Cognitive Radio Communications: A Survey

Sparsity Order Estimation and its Application in Compressive Spectrum Sensing for Cognitive Radios

Recursive Reconstruction of Sparse Signal Sequences

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