Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

Xu, Qiangrong; Sheng, Zhiqiang; Fang, Yong; Zhang, Liming

doi:10.3390/s21041229

Cited by 10 publications

(3 citation statements)

References 31 publications

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“…먼저 많은 계산량과 메모리를 필 요로 한다 [4] . 두 번째로 센싱 행렬식의 필수 요구 조건인 ristricted isometry property(RIP) 조건을 검증하는 효율적인 알고리즘이 없어서 성능을 확신하기 어렵다 [5] . 결정 센싱 행렬식(deterministic sensing matrix)은 메모리 문제를 해결 하며 빠르게 구현할 수 있는 구조로, 앞의 랜덤 센싱 행렬 식의 단점을 보완할 수 있다 [6] .…”

Section: ⅰ 서 론unclassified

Random Hybrid Chirp Sensing Matrix Implementation for Fast Compressive Sensing SAR Processing

Jo¹,

Chun²,

Ban³

et al. 2021

J. Korean Inst. Electromagn. Eng. Sci.

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Compressive sensing uses the sparsity of signals and the incoherence of sensing matrices. The use of random sensing matrices ensures an easy configuration and a high probability of reconstruction, but there is no optimum algorithm that can avoid the lengthy computation time and high memory consumption burden. Deterministic sensing matrix equations are known to mitigate these problems, and among others, chirp sensing matrices can help to achieve fast data recovery. However, most deterministic sensing matrices suffer from increased internal interference compared with that of random sensing matrix groups, and consequently result in degraded performance. In this paper, we propose a novel compressive sensing reconstruction method that enables the acquisition of excellent sparse signal reconstruction performance of existing random sensing matrices and signal processing acceleration performance through deterministic sensing matrices. Accordingly, we propose a method that contributes to the increase in the vast amount of data that has been a chronic problem with SAR(Synthetic Aperture Radar) images and the acceleration of the processing speed.

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Section: ⅰ 서 론unclassified

Random Hybrid Chirp Sensing Matrix Implementation for Fast Compressive Sensing SAR Processing

Jo¹,

Chun²,

Ban³

et al. 2021

J. Korean Inst. Electromagn. Eng. Sci.

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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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“…Elad [51] launched an algorithmic design for a sensing matrix by minimizing the average measure of the coherence iteratively. In [52]− [55], several algorithms have been proposed for optimizing a sensing matrix, where each one attempts to approximate its Gram matrix to that of an equiangular tight frame (ETF) [56]. In [57], Chen et al demonstrated that a unit-norm tight frame is a closest design of a nearly orthogonal matrix.…”

Section: Introductionmentioning

confidence: 99%

Design of Non-Orthogonal Sequences Using a Two-Stage Genetic Algorithm for Grant-Free Massive Connectivity

Yu¹

2021

Preprint

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In massive machine-type communications (mMTC), grant-free access is a key enabler for a massive number of users to be connected to a base station with low signaling overhead and low latency. In this paper, a two-stage genetic algorithm (GA) is proposed to design a new set of user-specific, non-orthogonal, unimodular sequences for uplink grant-free access. The firststage GA is to find a subsampling index set for a partial unitary matrix that can be approximated to an equiangular tight frame. Then in the second-stage GA, we try to find a sequence to be masked to each column of the partial unitary matrix, in order to reduce the peak-to-average power ratio of the resulting columns for multicarrier transmission. Finally, the masked columns of the matrix are proposed as new non-orthogonal sequences for uplink grant-free access. Simulation results demonstrate that the non-orthogonal sequences designed by our two-stage GA exhibit excellent performance for compressed sensing based joint activity detection and channel estimation in uplink grant-free access. Compared to algebraic design, this GA-based design can present a set of good non-orthogonal sequences of arbitrary length, which provides more flexibility for uplink grant-free access in mMTC.Index Terms-Compressed sensing, genetic algorithm, grantfree access, machine-type communications, non-orthogonal multiple access, peak-to-average power ratio.

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Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

Cited by 10 publications

References 31 publications

Random Hybrid Chirp Sensing Matrix Implementation for Fast Compressive Sensing SAR Processing

Random Hybrid Chirp Sensing Matrix Implementation for Fast Compressive Sensing SAR Processing

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

Design of Non-Orthogonal Sequences Using a Two-Stage Genetic Algorithm for Grant-Free Massive Connectivity

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