Deterministic Construction of Compressed Sensing Matrices from Protograph LDPC Codes

Zhang, Jun; Han, Guangjie; Fang, Yi

doi:10.1109/lsp.2015.2447934

Cited by 48 publications

(24 citation statements)

References 23 publications

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“…Both RIP [16][17][18][19] and coherence [9][10][11][12][13][20][21][22][23][24][25][26][27] are important tools to analyze the property of measurement matrices. In this paper, coherence will be adopted to analyze and illustrate the property of constructed measurement matrices, because it is easier to compute.…”

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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Section: Lemma 11mentioning

confidence: 99%

Binary Sequence Family for Chaotic Compressed Sensing

2019

KSII TIIS

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“…Similarly, Xu et al 28 developed methods to minimize the mutual coherence between the projection matrix and signal dictionary that leads to improved sparse recovery. Zhang et al 29 proposed a class of sparse binary sensing matrices based on the photograph LowDensity Parity-Check (LDPC) codes and analyzed recovery performance as a function of mutual coherence. In that work, it was shown that there is a direct correlation between low mutual coherence and the probably of exact recovery.…”

Section: Sensing Matrix Analyticsmentioning

confidence: 99%

A performance metric for screen selection with the acoustic single pixel imager

Rogers

Edelmann

2018

The Journal of the Acoustical Society of America

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In the recent literature, an Acoustic Single-Pixel Imager has been successfully developed for source localization in a two-dimensional waveguide. Source bearing angle estimation was carried out by applying sparse recovery techniques on sensor measurements taken over different imaging screens. This paper shows that the Mutual Coherence of the sensing matrix can be used as a metric to predict the source localization capability of the single-pixel imaging system. In particular, this paper's analysis focuses on the sparsity of open cells within the imaging screen and the number of imaging screens used to maximize the probability of correct detection over varying levels of source sparsity. In this work, a simulation environment to demonstrate how the mutual coherence of the sensing matrix correlates with source localization performance over source sparsity, sparsity of open screen cells, and number of measurements used for sparse recovery is developed. The analysis shows that the leading factor in source localization performance gains is primarily from the number of imaging screens used to measure the acoustic wave-field.

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“…Algebraic curves like elliptic curves can also be used to construct the deterministic measurement matrices [13]. LDPC code is another kind of method for constructing the deterministic measurement matrices [14]. All these methods only need to store some parameters rather than the whole matrix, but the measurement matrix has to be generated in real-time.…”

Section: Related Workmentioning

confidence: 99%

“…From (14) and (15), the low bound of one STP-CS key storage space is smaller than that of one traditional CS key storage space, when ̸ = 1. According to (4) and (5), is a column vector of dimension / .…”

Section: Performance Analysismentioning

confidence: 99%

“…Another kind of CS encryption can save storage space by storing matrix generation parameters as the secret key rather than the whole matrix [11,12]. This kind of CS encryption generates matrices by deterministic methods such as algebraic curves [13], coding (LDPC, BCH) [14], and chaotic systems (Chebyshev, Logistic, and Tent) [15,16]; it can save huge storage space compared with keeping the whole matrix. However, using this method, users have to generate the matrix before encryption for each transmission.…”

Section: Introductionmentioning

confidence: 99%

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Semitensor Product Compressive Sensing for Big Data Transmission in Wireless Sensor Networks

Peng

Tian

Kurths

2017

Mathematical Problems in Engineering

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Big data transmission in wireless sensor network (WSN) consumes energy while the node in WSN is energy-limited, and the data transmitted needs to be encrypted resulting from the ease of being eavesdropped in WSN links. Compressive sensing (CS) can encrypt data and reduce the data volume to solve these two problems. However, the nodes in WSNs are not only energy-limited, but also storage and calculation resource-constrained. The traditional CS uses the measurement matrix as the secret key, which consumes a huge storage space. Moreover, the calculation cost of the traditional CS is large. In this paper, semitensor product compressive sensing (STP-CS) is proposed, which reduces the size of the secret key to save the storage space by breaking through the dimension match restriction of the matrix multiplication and decreases the calculation amount to save the calculation resource. Simulation results show that STP-CS encryption can achieve better performances of saving storage and calculation resources compared with the traditional CS encryption.

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Deterministic Construction of Compressed Sensing Matrices from Protograph LDPC Codes

Cited by 48 publications

References 23 publications

Binary Sequence Family for Chaotic Compressed Sensing

Binary Sequence Family for Chaotic Compressed Sensing

A performance metric for screen selection with the acoustic single pixel imager

Semitensor Product Compressive Sensing for Big Data Transmission in Wireless Sensor Networks

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