Compressed Sensing With Combinatorial Designs: Theory and Simulations

Bryant, Darryn; Colbourn, Charles J.; Horsley, Daniel; Catháin, Padraig Ó

doi:10.1109/tit.2017.2717584

Cited by 12 publications

(6 citation statements)

References 23 publications

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“…A natural class of candidates would be the incidence matrices of t-(v, k, λ) designs (see [4] for example). Some related work is contained in [5,6].…”

Section: Discussionmentioning

confidence: 99%

“…But to date, constructions meeting all three criteria have either been asymptotic in nature (i.e., the results only produce matrices that are too large for practical implementations), or are known only to exist for a very restricted range of parameters. This investigation was inspired by work of the second author on constructions of sparse CS matrices from pairwise balanced designs and complex Hadamard matrices [6,5]. Some related work on constructing CS matrices from finite geometry is contained in [20,37].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sparsification of Matrices and Compressed Sensing

Hegarty¹,

Catháin²,

Zhao³

2018

Irish Math. Soc. Bull.

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Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon-Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and compressed sensing has emerging applications in medical imaging, big data, and statistics. Finding practical matrix constructions and computationally efficient recovery algorithms for compressed sensing is an area of intense research interest. Many probabilistic matrix constructions have been proposed, and it is now well known that matrices with entries drawn from a suitable probability distribution are essentially optimal for compressed sensing.Potential applications have motivated the search for constructions of sparse compressed sensing matrices (i.e., matrices containing few non-zero entries). Various constructions have been proposed, and simulations suggest that their performance is comparable to that of dense matrices. In this paper, extensive simulations are presented which suggest that sparsification leads to a marked improvement in compressed sensing performance for a large class of matrix constructions and for many different recovery algorithms.

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“…A natural class of candidates would be the incidence matrices of t-(v, k, λ) designs (see [4] for example). Some related work is contained in [5,6].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparsification of Matrices and Compressed Sensing

Hegarty¹,

Catháin²,

Zhao³

2018

Irish Math. Soc. Bull.

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“…3) For random matrices with small dimensions, fine tuning of the measurement matrix is essential [23]. 4) Random matrices may not display a proper performance in some applications where the quality of service is needed to be guaranteed [14].…”

Section: B Motivationmentioning

confidence: 99%

A New Approach to Design Sensing Matrix Based on the Sparsity Constant With Applications to Computed Tomography

2019

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Using random sensing matrices imposes some constraints on applying compressed sensing in practical applications such as computed tomography, high resolution radars, synthetic aperture radars and other imaging systems. On the other hand, the lack of certain criteria to measure the suitability of a sensing matrix in compressed sensing, makes designing of the relevant sampling system difficult; so, researchers have turned largely toward trial and error methods for designing such sensing matrices. In this paper, we propose a constructive approach to design measurement matrices which largely overcomes the aforementioned drawbacks and presents some simple and calculable measures for sensing matrices. The presented algorithm outperforms various random and deterministic approaches in designing compressed sensing matrices due to its recoverability performance and generality, at the same time, our scheme benefits from the fact that the sensing matrix performance is easily determined. Based on the proposed method and despite all constrains that exist in measurement matrices in different problems, we can design sensing matrices in a unified manner with even better performance than that of random scenarios. In addition, we apply the proposed algorithm in computed tomography where the measurement matrix is a structured matrix and our method can gain much improvement in the recoverability performance. Furthermore, this article provides parameters that affect the performance of a sensing matrix, which theoretically clarifies the causes of the good recoverability performance of Gaussian matrices and the poor recoverability performance of periodic matrices. INDEX TERMS Compressed sensing, sparsity constant, measurement matrix design, transitivity of correlations, computed tomography.

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“…In recent years, many researchers have put forward many principles and methods to construct [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and optimize [34][35][36] measurement matrices. This paper mainly studies the construction method of deterministic measurement matrices.…”

Section: Introductionmentioning

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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Compressed Sensing With Combinatorial Designs: Theory and Simulations

Cited by 12 publications

References 23 publications

Sparsification of Matrices and Compressed Sensing

Sparsification of Matrices and Compressed Sensing

A New Approach to Design Sensing Matrix Based on the Sparsity Constant With Applications to Computed Tomography

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

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