Deterministic Sensing Matrices Based on Multidimensional Pseudo-Random Sequences

Tang, Yan; Lv, Guonian; Yin, Kai

doi:10.1007/s00034-013-9701-5

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…For LFSR, different feedback polynomials generate distinct m-sequences [31]. For m-sequence, the properties of balance, excursion distribution and auto-correlation are similar to the basic properties of random sequence [32]. Therefore, m-sequence is the most widely used pseudorandom sequence.…”

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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“…For the convenience of the following discussion, we assume that the last element of x is 0, so the last column of A can be abandoned. Then (13) changes into…”

Section: Practical Implementationmentioning

confidence: 99%

“…In practical application, random sensing matrices usually imply random sampling in data acquisition, which is difficult to implement in hardware. Many scholars have become interested in finding deterministic RIP matrix constructions [13] [17]. A deterministic construction of sensing matrices was given by polynomials over finite fields and the RIP weaker than random matrices was proven [7].…”

Section: Introductionmentioning

confidence: 99%

A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

Huang

Zhang

2016

Circuits Syst Signal Process

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In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires random sampling in data acquisition, which is difficult to implement in hardware. By using these sensing matrices in harmonic detection, a deterministic sampling method is provided. The frequencies and amplitudes of the harmonic components are estimated from under-sampled data. The simulations show that this under-sampled method is feasible and valid in noisy environments.

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“…Therefore, this innovative theory of improving sampling efficiency has been of great interest in the fields of digital signal processing [11], optical imaging [12], medical imaging [13], radio communication [14], radar imaging [15], and pattern recognition [16]. The research conducted on compressed sensing comprises three main areas: (1) the sparse representation of original signals, with commonly used sparse transform methods such as the Fourier Transform (FT) [17], Discrete Cosine Transform (DCT) [18], and Wavelet Transform (DWT) [19]; (2) the design of the measurement matrix, including the random measurement matrix [20,21] and deterministic measurement matrix [22,23]; (3) reconstruction algorithms, such as the basis pursuit (BP) algorithm [24,25], matching pursuit (MP) algorithm [26], and orthogonal matching pursuit algorithm [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Research on Photon-Integrated Interferometric Remote Sensing Image Reconstruction Based on Compressed Sensing

Yong

Li²,

Feng

et al. 2023

Remote Sensing

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Achieving high-resolution remote sensing images is an important goal in the field of space exploration. However, the quality of remote sensing images is low after the use of traditional compressed sensing with the orthogonal matching pursuit (OMP) algorithm. This involves the reconstruction of the sparse signals collected by photon-integrated interferometric imaging detectors, which limits the development of detection and imaging technology for photon-integrated interferometric remote sensing. We improved the OMP algorithm and proposed a threshold limited-generalized orthogonal matching pursuit (TL-GOMP) algorithm. In the comparison simulation involving the TL-GOMP and OMP algorithms of the same series, the peak signal-to-noise ratio value (PSNR) of the reconstructed image increased by 18.02%, while the mean square error (MSE) decreased the most by 53.62%. The TL-GOMP algorithm can achieve high-quality image reconstruction and has great application potential in photonic integrated interferometric remote sensing detection and imaging.

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Deterministic Sensing Matrices Based on Multidimensional Pseudo-Random Sequences

Cited by 6 publications

References 12 publications

Binary Sequence Family for Chaotic Compressed Sensing

Binary Sequence Family for Chaotic Compressed Sensing

A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

Research on Photon-Integrated Interferometric Remote Sensing Image Reconstruction Based on Compressed Sensing

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