Analysis and design of irregular graphs for node-based verification-based recovery algorithms in compressed sensing

Eftekhari, Yaser; Banihashemi, Amir H.; Lambadaris, Ioannis

doi:10.1109/isit.2012.6281807

Cited by 5 publications

(17 citation statements)

References 17 publications

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“…Simultaneously, in the literature, some algorithms based on message propagation over graph representations of measurement matrices were shown to outperform the theoretical limits of the classical compressed sensing approach [4], e.g. the scheme proposed in [6] based on the approximate message passing (AMP) [7], and the verification-based algorithms [8], [9].…”

Section: Introductionmentioning

confidence: 99%

List message passing algorithm for noiseless compressed sensing

Javega¹,

Lamarca²

2015

2015 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)

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We propose a verification-based algorithm for noiseless Compressed Sensing that reconstructs the original signal operating on a sparse graph. The proposed scheme has affordable computational complexity and its performance is significantly better than previous verification-based algorithms and similar to AMP-based algorithms. We also show that the performance of a noiseless compressed sensing scheme when verification-based algorithms and a sparse matrix is employed to reconstruct the original signal can be upper bounded by the performance of a LDPC code employing the same parity matrix when correcting a codeword transmitted through a BEC.

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Section: Introductionmentioning

confidence: 99%

List message passing algorithm for noiseless compressed sensing

Javega¹,

Lamarca²

2015

2015 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)

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“…The threshold values and asymptotic results of [29] and [88] are also applicable to the proposed NB-VB algorithm in the context of zero-block detection, i.e., for a given degree distribution of the sensing graph, if the sparsity ratio is below the thresholds derived in [29] and [88], for regular and irregular graphs, respectively, the proposed algorithm will succeed with probability one in detecting all the zero (and non-zero) blocks. On the other hand, if the sparsity ratio is above the threshold, then the probability of detecting all the zero (and non-zero) blocks is zero.…”

Section: Sparse Signals: Noiseless Measurementsmentioning

confidence: 96%

“…The threshold, which is attributed to an ensemble of sensing graphs with a certain degree distribution, was obtained in [29] using a technique called density evolution. The analysis of [29] was then extended to irregular sensing graphs in [88] and it was shown that properly designed irregular graphs can substantially outperform the regular ones with the same under-sampling ratio. It is important to note that VB algorithms have so far been only applied to sparse (not necessarily block sparse) signal recovery.…”

Section: Sparse Signals: Noiseless Measurementsmentioning

confidence: 99%

“…Note that in the noiseless case, P W ZD = 0. Remark 6.3: In [88], irregular sensing graphs were designed that maximized the success threshold for a given under-sampling ratio and a given maximum variable node degree. Based on Remark 6.2, such sensing graphs will also be asymptotically optimal in the context of this work.…”

Section: Sparse Signals: Noiseless Measurementsmentioning

confidence: 99%

“…We consider two sets of sensing graphs, each consisting of an optimized irregular and a regular graph with the same under-sampling ratio. For the first set, the regular graph has d V = 4 and d M = 8, and the irregular graph has the degree distribution (λ(x), ρ(x)) = (0.896x 3 +0.04x 12 +0.064x 13 , x 8 ) [88]. For the second set, we have d V = 4 and d M = 5, for the regular graph, and (λ(x), ρ(x)) = (0.9x 3 + 0.1x 13…”

Section: Noiseless Scenariosmentioning

confidence: 99%

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Compressed Sensing of Block Sparse Signals with Application to Wideband Spectrum Sensing

Zeinalkhani¹

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Wideband spectrum sensing (WSS) is a significant challenge in cognitive radios (CRs) due to requirement of very high-speed analog-to-digital converters (ADCs), operating at or above the Nyquist rate. To alleviate the need for high sampling rates, compressed sensing can be applied to WSS. Compressed sensing is a signal processing technique to recover high dimensional signals from a fewer measurements than conventional sampling theory demands. In compressed sensing, the superior algorithms are the ones that can recover the signal with fewer measurements.In many applications of compressed sensing such as WSS, the signal has a block sparse structure which can be used to reduce the required sampling rate. Here, we propose a family of iterative algorithms for the recovery of block sparse signals, referred to as iterative reweighted 2 / 1 minimization algorithms (IR-2 / 1 ). As an example, we apply the proposed algorithms to WSS. Our simulation and analytical results on the recovery of both ideally and approximately block sparse signals show that the proposed iterative algorithms have significant advantages in terms of accuracy and the number of required measurements over the existing recovery methods at a small cost in computational complexity.The approximate message passing (AMP) algorithm of Donoho et al. has attracted much attention due to its remarkable performance/complexity trade-off. In this thesis, we also propose a weighting/reweighting scheme to improve the performance of AMP algorithm for the recovery of block sparse signals with known borders. For the case of unknown borders, we propose an iterative algorithm which combines a border detection scheme with a recovery algorithm for block sparse signals with known borders. Simulation results, both in noiseless and noisy scenarios, show a considerably better performance/complexity trade-off compared to other state-of-the-art recovery algorithms.Although the recovery methods can be applied to WSS for the spectrum reconstruction to detect the spectrum holes, to further reduce the sampling rate, one can iii find a sufficiently large fraction of spectrum holes without spectrum reconstruction. Here, we first propose a very low-complexity zero-block detection scheme that can detect a large fraction of spectrum holes from the sub-Nyquist samples, even when the undersampling ratio is very small. We then propose an iterative low-complexity scheme for the reliable detection of zero blocks in a block sparse signal. This scheme is based on the application of verification-based (VB) recovery algorithms in compressed sensing to block sparse signals. To apply both schemes to WSS, we devise a block sparse sensing matrix by designing a novel analog-to-information converter (AIC). The AIC, the sensing matrix and the VB algorithms can be optimized such that the largest number of zero blocks for a given number of measurements can be detected. These works introduce a new paradigm in the recovery of block sparse signals, where one is interested in partial detection of the complement ...

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Low-complexity detection of zero blocks in wideband spectrum sensing

Zeinalkhani

Banihashemi

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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Analysis and design of irregular graphs for node-based verification-based recovery algorithms in compressed sensing

Cited by 5 publications

References 17 publications

List message passing algorithm for noiseless compressed sensing

List message passing algorithm for noiseless compressed sensing

Compressed Sensing of Block Sparse Signals with Application to Wideband Spectrum Sensing

Low-complexity detection of zero blocks in wideband spectrum sensing

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