Design and Generalization Analysis of Orthogonal Matching Pursuit Algorithms

Hussain, Zakria; Shawe‐Taylor, John; Hardoon, David R.; Dhanjal, Charanpal

doi:10.1109/tit.2011.2158880

Cited by 18 publications

(12 citation statements)

References 32 publications

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“…For an acoustic emission signal The simulated underwater echo in Figure 3 is then compressed and reconstructed with CS. In this study, the discrete cosine transform [33,34] is used as the sparse matrix, and the reconstruction algorithm adopted is the orthogonal matching pursuit (OMP) [35][36][37]. The measurement matrix based on the cyclic direct product and QR decomposition is compared respectively with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix.…”

Section: Simulation Of Underwater Echo and Its Compression And Reconsmentioning

confidence: 99%

Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo

et al. 2018

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Compressive sensing is a very attractive technique to detect weak signals in a noisy background, and to overcome limitations from traditional Nyquist sampling. A very important part of this approach is the measurement matrix and how it relates to hardware implementation. However, reconstruction accuracy, resistance to noise and construction time are still open challenges. To address these problems, we propose a measurement matrix based on a cyclic direct product and QR decomposition (the product of an orthogonal matrix Q and an upper triangular matrix R). Using the definition and properties of a direct product, a set of high-dimensional orthogonal column vectors is first established by a finite number of cyclic direct product operations on low-dimension orthogonal “seed” vectors, followed by QR decomposition to yield the orthogonal matrix, whose corresponding rows are selected to form the measurement matrix. We demonstrate this approach with simulations and field measurements of a scaled submarine in a freshwater lake, at frequencies of 40 kHz–80 kHz. The results clearly show the advantage of this method in terms of reconstruction accuracy, signal-to-noise ratio (SNR) enhancement, and construction time, by comparison with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix. In particular, for weak signals with an SNR less than 0 dB, this method still achieves an SNR increase using less data.

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Section: Simulation Of Underwater Echo and Its Compression And Reconsmentioning

confidence: 99%

Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo

et al. 2018

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“…MP and OMP, two greedy algorithms originally proposed for sparse recovery problems, sequentially estimate the sparse channel by using a training sequence [14,28]. MP applies sequential forward selection to determine a sparse representation of the channel h by using a training sequence and its corresponding received signal.…”

Section: Performance Comparisonmentioning

confidence: 99%

“…In order to blindly estimate a sequence transmitted over a sparse channel, popular sparse channel estimation methods such as matching pursuit (MP), orthogonal matching pursuit (OMP), and basis pursuit (BP) [12][13][14] can be combined with the VA or stack algorithm using a joint channel estimation and data detection framework. As we show in Section 5, however, these conventional methods result in high complexity, particularly when signal to noise ratio (SNR) is low.…”

Section: Introductionmentioning

confidence: 99%

Blind sequential detection for sparse ISI channels

Zhou

Nelson

2018

EURASIP J. Adv. Signal Process.

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We present a computationally efficient blind sequential detection method for data transmitted over a sparse intersymbol interference channel. Unlike blind sequential detection methods designed for general channels, the proposed method exploits the channel sparsity by using estimated channel sparsity to assist in the detection of the transmitted sequence. A Gaussian mixture model is used to describe sparse channels, and two tree-search strategies are applied to estimate the channel sparsity and the transmitted sequence, respectively. To demonstrate the performance improvement achieved by the proposed blind detector, we compare it to conventional joint channel and sequence detection methods that use sparse channel estimation techniques. Simulation results show that the proposed detector not only reduces computational complexity compared to existing methods but also provides superior performance, particularly when the signal to noise ratio is low.

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“…Seeking for the sparse representation of a signal from the sensing matrix is a non-deterministic polynomial hard (NP-hard) problem. The orthogonal matching pursuit (OMP) [13] algorithm provide a way to solve the problem, we use this algorithm as the basis algorithm in this paper.…”

Section: Mathematical Model Of Csmentioning

confidence: 99%

“…If there N bits original signal in the processing time, there are 2 N P = possible forms of the signal. Then the transmitted signal can be expressed as (13).…”

Section: ) Dsss Signal Model and Its Sparse Representationmentioning

confidence: 99%

Adaptive multi-tone jamming suppression for DSSS communications based on compressive sensing

Xin

Zhang

Kou³

2015

2015 8th International Congress on Image and Signal Processing (CISP)

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The existing multi-tone jamming suppression algorithms for direct sequence spread spectrum (DSSS) communications are confined to the high sampling rate. The compressive sensing (CS) was applied to solve the problem. Firstly, the DSSS signal and multi-tone jamming sparse dictionary was built, the multi-tone jamming suppression algorithm used in compressed domain was designed. Secondly, due to the difficulty in getting the prior information of the sparse degree of the jamming, the adaptive multi-tone jamming suppression algorithm was designed by setting the control threshold. The theoretical basis of the algorithm were analyzed, the effectiveness of the algorithm was verified by computer simulation. The results show that the algorithm could suppress the multi-tone jamming effectively, the performance don't change over the jamming intensity, jamming quantity and jamming position. This will provide an effective method for the reconstruction of the compressed DSSS signal in the condition of the multi-tone jamming.

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Design and Generalization Analysis of Orthogonal Matching Pursuit Algorithms

Cited by 18 publications

References 32 publications

Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo

Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo

Blind sequential detection for sparse ISI channels

Adaptive multi-tone jamming suppression for DSSS communications based on compressive sensing

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