Arbitrary Block-Sparse Signal Reconstruction Based on Incomplete Single Measurement Vector

Yang, Enpin; Zhang, Tianhong; Wang, Qian; Qin, Kaiyu

doi:10.1007/s00034-017-0528-3

Cited by 3 publications

(7 citation statements)

References 23 publications

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“…, 푀 ) 푇 ∈ R 푀 is the additive noise. Given A and y, estimating x from y is named as the Single Measurement Vector (SMV) problem [1][2][3]25]. 1 minimization algorithms [26][27][28] and GP algorithms are proposed to solve the SMV problem.…”

Section: Single Measurement Vector (Smv)mentioning

confidence: 99%

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

Liu

Hua

Zhu

et al. 2018

Mathematical Problems in Engineering

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In solving the partial Fourier Multiple Measurement Vectors (FMMV) problem, existing greedy pursuit algorithms such as Simultaneous Orthogonal Matching Pursuit (SOMP), Simultaneous Subspace Pursuit (SSP), Hybrid Matching Pursuit (HMP), and Forward-Backward Pursuit (FBP) suffer from low recovery ability or need sparsity as a prior information. This paper combines SOMP and FBP to propose a Hybrid Orthogonal Forward-Backward Pursuit (HOFBP) algorithm. As an iterative algorithm, each iteration of HOFBP consists of two stages. In the first stage, indices selected by SOMP are added to the support set. In the second stage, the support set is shrank by removing indices. The choice of and is critical to the performance of this algorithm. The simulation results showed that, by using proper parameters, HOFBP has better performance than other greedy pursuit algorithms at the expense of more computing time in some cases. HOFBP does not need sparsity as a prior knowledge.

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Section: Single Measurement Vector (Smv)mentioning

confidence: 99%

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

Liu

Hua

Zhu

et al. 2018

Mathematical Problems in Engineering

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“…The Xðt; fÞ reconstruction part of the algorithm is the BMP algorithm [16,17], which is a greedy iteration algorithm and adopts a stagewise strategy to reconstruct the signal. The details of this part are introduced in the next section, because this part is similar with the MBMP algorithm in Section 3.…”

Section: The Chirp Rate Estimation Algorithmmentioning

confidence: 99%

“…The details of this part are introduced in the next section, because this part is similar with the MBMP algorithm in Section 3. We also refer the reader to our previous work [16,17] for details of BMP.…”

Section: The Chirp Rate Estimation Algorithmmentioning

confidence: 99%

“…Note that although the de-chirped signal is processed by MWC, the signal reconstruction algorithm adopted by our system differs from that of the original MWC. Our another contribution is the signal reconstruction algorithm, which evolves from our previous work [16,17]: the block matching pursuit (BMP) algorithm, and it is named multiple measurements BMP (MBMP) algorithm. The proposed reconstruction algorithm guarantees an outstanding reconstruction performance even if the chirp rate is not exactly estimated.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed reconstruction algorithm guarantees an outstanding reconstruction performance even if the chirp rate is not exactly estimated. Compared with the BMP in [16,17], the most creative feature of the algorithm in this letter is the adaptive halting condition which makes the sampling system more practical.…”

Section: Introductionmentioning

confidence: 99%

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A novel compressive sampling system for chirp signal

Yang

Yan

Qin

2017

IEICE Electron. Express

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In this letter, a compressive sampling system, which can acquire chirp signal without the prior information of carrier frequency and chirp rate, is proposed. The system first estimates the chirp rate based on windowed modulated wideband converter (MWC). When chirp rate is derived, the system can de-chirp the target signal. Then, the de-chirped signal is acquired by sampling module of the system. Finally, basedon samples, the original signal can be reconstructed by a greedy iteration algorithm which has an adaptive halting condition. Simulation results show the system is capable of estimating chirp rate and reconstructing original signal.

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Marine Radar Image Processing of Compressed Sensing Based on Arbitrary Block Statistical Histogram and Dynamic Dictionary

Liu

Pang

Fu³

et al. 2019

IEEE Access

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In compressed sensing (CS), the absolute value of the inner product of signal and atom (or dictionary) is used to select atom (or dictionary); the atoms (or dictionaries) with larger absolute values of inner product are selected to decompose and reconstruct signals. This characteristic usually makes it impossible to distinguish the edges of objects (or targets) in some complex cases, especially when the density of objects is very high. For example: let signal, ψ 3 and ψ 4 denote several sparse basis matrices (i.e., sparse dictionaries);T are the sparse bases (i.e., atoms) from these sparse basis matrices (i.e., dictionaries), respectively. For signal x 1 , ψ 4l (or ψ 4 ) is selected instead of ψ 2j (or ψ 2 ); likewise, for x 2 , ψ 4l (or ψ 4 ) will be selected instead of ψ 3j (or ψ 3 ) and ψ 1i (or ψ 1 ). This causes the edge of the object to be unrecognizable. Another example is in l p regularization, it is not necessarily the optimal case: the smaller the value of −1 d x 0 , the better the sparse basis matrix (i.e., dictionary), or the larger the weighing parameter. At present, the inner product is used to process almost all signals in CS. Choosing the dictionary that matches the signal best rather than the dictionary with the maximum inner product value can reconstruct the signal more accurately. In order to overcome the above shortcoming, we propose a fully automatic radar image processing algorithm of CS based on arbitrary block statistical histogram and dynamic dictionary. We use arbitrary block statistical histogram to calculate the non-zero block numbers of different sizes, which can better choose the appropriate sparse base (or dictionary) for the signal. Furthermore, the better measurement vector y can be obtained, and the signal can be reconstructed more accurately than the state-of-the-art methods at the receiving end. To realize the proposed method, we construct objective functions and flow charts for noiseless and noisy signals, respectively. In our method, for noiseless signal, discarding the sub-images that do not contain objects can reduce running time; for noisy signal, according to the theory of wavelet, choosing the appropriate wavelet (i.e., wavelet basis) can usually suppress noise. Our proposed algorithm can overcome the above shortcoming of CS in using the absolute value of the inner product, reduce running time, suppressnoise, and improve the signal-tonoise ratio (SNR). The simulation results show that our method is superior to the state-of-the-art methods. INDEX TERMSCompressed sensing (CS), inner product, shortcoming, arbitrary block statistical histogram, dynamic dictionary, stagewise orthogonal matching pursuit algorithm (StOMP).

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Arbitrary Block-Sparse Signal Reconstruction Based on Incomplete Single Measurement Vector

Cited by 3 publications

References 23 publications

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

A novel compressive sampling system for chirp signal

Marine Radar Image Processing of Compressed Sensing Based on Arbitrary Block Statistical Histogram and Dynamic Dictionary

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