Robustness of orthogonal matching pursuit for multiple measurement vectors in noisy scenario

Ding, Jie; Chen, Laming; Gu, Yuantao

doi:10.1109/icassp.2012.6288748

Cited by 13 publications

(8 citation statements)

References 11 publications

(22 reference statements)

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“…Regarding older works, it is also worth pointing out that the ERC δ |S|+1 < 1/((1+ √ 2) |S|), first obtained in [17, Theorem 5.2] for OMP, has been shown to remain valid for SOMP in [11,Corollary 1]. Thereby, the authors of [11] also proved that the older ERC δ |S|+1 < 1/(3 |S|), initially derived in [8, Theorem 3.1] for OMP, remains correct for SOMP as δ |S|+1 < 1/(3 |S|) is implied by δ |S|+1 < 1/((1 + √ 2) |S|). Very recently, (ERC2) was extended to SOMP in [27,Remark 1].…”

Section: Contribution and Related Workmentioning

confidence: 93%

On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

Determe

Louveaux

Jacques

et al. 2016

IEEE Signal Process. Lett.

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Abstract-Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC). In this paper, three of the most recent ERC for OMP are examined. The contribution is to show that these ERC remain valid for a generalization of OMP, entitled simultaneous orthogonal matching pursuit (SOMP), that is capable to process several measurement vectors simultaneously and return a common support estimate for the underlying sparse vectors. The sharpness of the bounds is also briefly discussed in light of previous works focusing on OMP.

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Section: Contribution and Related Workmentioning

confidence: 93%

On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

Determe

Louveaux

Jacques

et al. 2016

IEEE Signal Process. Lett.

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“…Modifying from (25) and ignoring the quantization error, we can get a delay-quantized on-grid model for the measurements from N d OFDM symbols as Y(n t , n r ) = C τ P(n t , n r )D g (n t , n r )V d…”

Section: B High-resolution Approach: 1d Compressive Sensingmentioning

confidence: 99%

“…Resolution for τ and f D, may be improved by using traditional super-resolution spectrum analysis techniques such as 2D-ESPRIT [16] and 2-D Matrix Pencil [17], [18], based on the signal model in (25). However, these techniques require the number of measurements to be larger than the number of multipath signals in each dimension.…”

Section: B High-resolution Approach: 1d Compressive Sensingmentioning

confidence: 99%

Multibeam for Joint Communication and Radar Sensing Using Steerable Analog Antenna Arrays

Zhang

Huang

Yuan

et al. 2019

IEEE Trans. Veh. Technol.

194

145

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Beamforming has great potential for joint communication and sensing (JCAS), which is becoming a demanding feature on many emerging platforms such as unmanned aerial vehicles and smart cars. Although beamforming has been extensively studied for communication and radar sensing respectively, its application in the joint system is not straightforward due to different beamforming requirements by communication and sensing. In this paper, we propose a novel multibeam framework using steerable analog antenna arrays, which allows seamless integration of communication and sensing. Different to conventional JCAS schemes that support JCAS using a single beam, our framework is based on the key innovation of multibeam technology: providing fixed subbeam for communication and packetvarying scanning subbeam for sensing, simultaneously from a single transmitting array. We provide a system architecture and protocols for the proposed framework, complying well with modern packet communication systems with multicarrier modulation. We also propose low-complexity and effective multibeam design and generation methods, which offer great flexibility in meeting different communication and sensing requirements. We further develop sensing parameter estimation algorithms using conventional digital Fourier transform and 1D compressive sensing techniques, matching well with the multibeam framework. Simulation results are provided and validate the effectiveness of our proposed framework, beamforming design methods and the sensing algorithms. 2 protocols, a BF design methodology, multibeam generation and updating algorithms, and sensing algorithms, to achieve large field-of-view (range in directions), flexible and accurate sensing with controllable and insignificant compromise on communication performance.Our main contributions in this paper are as follows, with a focus on multibeam with two subbeams:• We propose a system architecture and protocols for implementing multibeam JCAS technology, with the use of two analog arrays. The two arrays, spatially widely separated, are introduced mainly to suppress leakage signal from the transmitter to receiver, so that the receiver can work all the time, transiting between communication and sensing modes. The proposed framework fully complies with a conventional time division duplex (TDD) communication system and reuses the TDD timeslot. This is detailed in Section II; • We provide a BF design methodology to enable the integration of beam-scanning based sensing with fixedbeam based communication functions. We also present a generalized Least Squares (LS) BF solution for generating beams with desired shape. This is discussed in Section III; • Detailed methods for generating and updating multibeam BF vectors are developed. The methods offer flexibility in meeting different and time-varying requirements for communication and sensing, capability in constructively combining communication and sensing subbeams for communication purpose, and simplicity in updating BF vectors. The details are presented in Section IV...

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“…Similarly, there exist three main approaches for solving MMVs. The first approach is the extended version of the greedy-based SMV solvers such as MMV basic matching pursuit (M-BMP), MMV order recursive matching pursuit (M-ORMP), and MMV orthogonal matching pursuit (M-OMP) [ 17 , 18 , 19 ]. The second approach is relaxed-to-be-convex algorithms such as the joint

approximation algorithm (JLZA) [ 20 ].…”

Section: Background and Introductionmentioning

confidence: 99%

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

Shekaramiz

Moon

Gunther

2019

Entropy

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We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs.

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Robustness of orthogonal matching pursuit for multiple measurement vectors in noisy scenario

Cited by 13 publications

References 11 publications

On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

Multibeam for Joint Communication and Radar Sensing Using Steerable Analog Antenna Arrays

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

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