On the Spark of Binary LDPC Measurement Matrices From Complete Protographs

Liu, Haiyang; Zhang, Hao; Ma, Lianrong

doi:10.1109/lsp.2017.2749043

Cited by 10 publications

(3 citation statements)

References 27 publications

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“…The specific proof process can be found in Appendix A. Notably, on the one hand, the results show that there is a significant relationship between the size of the circulant permutation matrix (CPM) and the girth of the measurement matrix, it is because the codes with large girth have better bit-error rate performances; on the other hand, there is a significant relationship between the girth of the measurement matrix and the performance of the CS method [47][48][49].…”

Section: Girth Analysismentioning

confidence: 99%

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

2023

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It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including good reconstruction performance, low memory cost and low computing resources. Low-density-parity check (LDPC) codes and CS codes can be closely related. This paper presents a method of constructing compressed sensing measurement matrices based on quasi-cyclic (QC) LDPC codes and arithmetic sequence sets. The cyclic shift factor in each submatrix of QC-LDPC is determined by arithmetic sequence sets. Compared with random matrices, the proposed method has great advantages because it is generated based on a cyclic shift matrix, which requires less storage memory and lower computing resources. Because the restricted isometric property (RIP) is difficult to verify, mutual coherence and girth are used as computationally tractable indicators to evaluate the measurement matrix reconstruction performance. Compared with several typical matrices, the proposed measurement matrix has the minimum mutual coherence and superior reconstruction capability of CS signal according to one-dimensional (1D) signals and two-dimensional (2D) image simulation results. When the sampling rate is 0.2, the maximum (minimum) gain of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) is up to 2.89 dB (0.33 dB) and 0.031 (0.016) while using 10 test images. Meanwhile, the reconstruction time is reduced by nearly half.

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Section: Girth Analysismentioning

confidence: 99%

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

2023

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“…Although deterministic matrices may need a lot of complex mathematical operations during their construction, all elements of these matrices can be computed and generated on the fly only once, thus providing storage efficiency. Recently, many researchers have exploited some existing theories and techniques to construct deterministic measurement matrices, such as Euler Squares [9], extremal set theory [10], near orthogonal systems [12], chaotic systems [20][21][22], Legendre sequences [23], optimal codebooks [24], bipartite graph [25], low-density parity-check (LDPC) codes [13,14,26,28], equiangular tight frame theory [27], Reed-Muller sequences [29] and sparse fast Fourier transform [30]. In particular, Sasmal et al [11] proposed an optimal deterministic binary CS matrices by using a specialized composition rule which exploits the properties of existing binary matrices.…”

Section: Lemma 11mentioning

confidence: 99%

Binary Sequence Family for Chaotic Compressed Sensing

2019

KSII TIIS

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It is significant to construct deterministic measurement matrices with easy hardware implementation, good sensing performance and good cryptographic property for practical compressed sensing (CS) applications. In this paper, a deterministic construction method of bipolar chaotic measurement matrices is presented based on binary sequence family (BSF) and Chebyshev chaotic sequence. The column vectors of these matrices are the sequences of BSF, where 1 is substituted with-1 and 0 is with 1. The proposed matrices, which exploit the pseudo-randomness of Chebyshev sequence, are sensitive to the initial state. The performance of proposed matrices is analyzed from the perspective of coherence. Theoretical analysis and simulation experiments show that the proposed matrices have limited influence on the recovery accuracy in different initial states and they outperform their Gaussian and Bernoulli counterparts in recovery accuracy. The proposed matrices can make the hardware implement easy by means of linear feedback shift register (LFSR) structures and numeric converter, which is conducive to practical CS.

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“…In [22], Wang et al provided deterministic CS matrices based on optimal codebooks and specific codes. In [23], Liu et al involved the deterministic binary LDPC measurement matrices from complete protographs. In [24], Wang et al involved the deterministic measurement matrices by second-order Reed-Muller sequences.…”

Section: Introductionmentioning

confidence: 99%

Deterministic Bipolar Compressed Sensing Matrices from Binary Sequence Family

Lu¹,

Chen²,

Xu³

2020

KSII TIIS

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For compressed sensing (CS) applications, it is significant to construct deterministic measurement matrices with good practical features, including good sensing performance, low memory cost, low computational complexity and easy hardware implementation. In this paper, a deterministic construction method of bipolar measurement matrices is presented based on binary sequence family (BSF). This method is of interest to be applied for sparse signal restore and image block CS. Coherence is an important tool to describe and compare the performance of various sensing matrices. Lower coherence implies higher reconstruction accuracy. The coherence of proposed measurement matrices is analyzed and derived to be smaller than the corresponding Gaussian and Bernoulli random matrices. Simulation experiments show that the proposed matrices outperform the corresponding Gaussian, Bernoulli, binary and chaotic bipolar matrices in reconstruction accuracy. Meanwhile, the proposed matrices can reduce the reconstruction time compared with their Gaussian counterpart. Moreover, the proposed matrices are very efficient for sensing performance, memory, complexity and hardware realization, which is beneficial to practical CS.

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On the Spark of Binary LDPC Measurement Matrices From Complete Protographs

Cited by 10 publications

References 27 publications

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

Binary Sequence Family for Chaotic Compressed Sensing

Deterministic Bipolar Compressed Sensing Matrices from Binary Sequence Family

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