Compressive Sensing With Prior Information: Requirements and Probabilities of Reconstruction in 𝓁<sub>1</sub>- Minimization

Miosso, Cristiano Jacques; Borries, Ricardo von; Pierluissi, Joseph H.

doi:10.1109/tsp.2012.2231076

Cited by 30 publications

(19 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The error of the reconstructed image is higher than the reconstruction errors reported in [MvBP13] and [MvBP09]; however, the result in Figure 8 was obtained under more restrictive conditions. To limit the computation time needed for image reconstruction, we have to limit the size of the images and the number of measurements used in the reconstruction.…”

Section: A Amentioning

confidence: 55%

Detection and Imaging of Improvised Explosive Devices

Borries¹

2014

View full text Add to dashboard Cite

Section: A Amentioning

confidence: 55%

Detection and Imaging of Improvised Explosive Devices

Borries¹

2014

View full text Add to dashboard Cite

“…This problem is an ordinary sparse coding problem and many algorithms have been proposed [17]. However, the recent CS researches reveal that the use of the additional prior information about the sparse representation's support is shown to have advantages in terms of number of required measurements, convergence time and number of iterations [18,19]. Nonetheless, in DFPL applications this information is not easy to be obtained, since the target to be tracked is generally uncooperative.…”

Section: Cs Reconstruction Algorithm With Prior Informationmentioning

confidence: 99%

“…The idea of this method is to introduce weights dependent on the prior information on the positions of nonzero coefficients in the sparse domain into the traditional basis pursuit (BP) algorithm, so that nonzero coefficients in the prior region are favored. Motivated by iteratively reweighted idea in [18,19], the sparse vector x t can then be reconstructed from the measurements ∆R t by solving…”

Section: Cs Reconstruction Algorithm With Prior Informationmentioning

confidence: 99%

Device-Free Electromagnetic Passive Localization With Frequency Diversity

Ke¹,

Yuan

Zhang³

et al. 2016

PIER M

View full text Add to dashboard Cite

Abstract-As an emerging wireless localization technique, the electromagnetic passive localization without the need of carrying any device, named device-free passive localization (DFPL) technique has drawn considerable research attention. The DFPL technique detects shadowed links in the monitored area and realizes localization with the received signal strength (RSS) measurements of these links. However, the current RSS-based DFPL techniques have two major challenges: one is that the RSS signal is particularly sensitive to noise, and the other is that it needs a sufficient number of nodes to provide enough RSS measurements of wireless links to guarantee good performance. To overcome these problems, in this paper we take advantage of compressive sensing (CS) theory to handle the spatial sparsity of the DFPL problem for reducing the number of nodes required by DFPL systems and exploit the frequency diversity technique to deal with the problem of the RSS sensitivity. Meanwhile, inspired by the fact that the target's movement is continuous and that the target's current location must be around the last location, we add prior information on the support region into the sparse reconstruction process for enhancing sparse reconstruction performance. The effectiveness and robustness of the proposed scheme are demonstrated by experimental results where the proposed algorithm yields substantial improvement for localization performance.

show abstract

“…This formulation encourages a solution with more zeros outside , and thus it may recover the signal more accurately than traditional CS does for signals whose support includes . Based on sufficient condition [19,22,23] for CS-PKS, the number of measurements required for CS-PKS is less than that required for traditional CS, and the more the support is known, the fewer the measurements needed are. The robustness of truncated minimization in noisy case has been discussed in [20][21][22].…”

Section: Compressed Spectrum Reconstruction With Partiallymentioning

confidence: 99%

Distributed Compressed Spectrum Sensing via Cooperative Support Fusion

Zha

Huang

Liu

et al. 2013

International Journal of Distributed Sensor Networks

View full text Add to dashboard Cite

Spectrum sensing in wideband cognitive radio (CR) networks faces several significant practical challenges, such as extremely high sampling rates required for wideband processing, impact of frequency-selective wireless fading and shadowing, and limitation in power and computing resources of single cognitive radio. In this paper, a distributed compressed spectrum sensing scheme is proposed to overcome these challenges. To alleviate the sampling bottleneck, compressed sensing mechanism is used at each CR by utilizing the inherent sparsity of the monitored wideband spectrum. Specifically, partially known support (PKS) of the sparse spectrum is incorporated into local reconstruction procedure, which can further reduce the required sampling rate to achieve a given recovery quality or improve the quality given the same sampling rate. To mitigate the impact of fading and shadowing, multiple CRs exploit spatial diversity by exchanging local support information among them. The fused support information is used to guide local reconstruction at individual CRs. In consideration of limited power per CR, local support information percolates over the network via only one-hop local information exchange. Simulation results testify the effectiveness of the proposed scheme by comparing with several existing schemes in terms of detection performance, communication load, and computational complexity. Moreover, the impact of system parameters is also investigated through simulations.

show abstract

Compressive Sensing With Prior Information: Requirements and Probabilities of Reconstruction in 𝓁₁- Minimization

Cited by 30 publications

References 25 publications

Detection and Imaging of Improvised Explosive Devices

Detection and Imaging of Improvised Explosive Devices

Device-Free Electromagnetic Passive Localization With Frequency Diversity

Distributed Compressed Spectrum Sensing via Cooperative Support Fusion

Contact Info

Product

Resources

About

Compressive Sensing With Prior Information: Requirements and Probabilities of Reconstruction in 𝓁1- Minimization

Cited by 30 publications

References 25 publications

Detection and Imaging of Improvised Explosive Devices

Detection and Imaging of Improvised Explosive Devices

Device-Free Electromagnetic Passive Localization With Frequency Diversity

Distributed Compressed Spectrum Sensing via Cooperative Support Fusion

Contact Info

Product

Resources

About

Compressive Sensing With Prior Information: Requirements and Probabilities of Reconstruction in 𝓁₁- Minimization