[1]LI Xiali,WU Licheng,FAN Yanming.Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware[J].CAAI Transactions on Intelligent Systems,2017,12(3):279-285.[doi:10.11992/tis.201606037]
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Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 12 Number of periods: 2017 3 Page number: 279-285 Column: 学术论文—机器感知与模式识别 Public date: 2017-06-25
Title:
Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware
Author(s):
LI Xiali;  WU Licheng;  FAN Yanming
School of Information Engineering, Minzu University of China, Beijing 100081, China
Keywords:
image processing; machine vision; compressed sensing; sampling and reconstruction; measurement matrix; sequence partial Hadamard; sequence pseudo-random; restricted isometry property
CLC:
TP391
DOI:
10.11992/tis.201606037
Abstract:
In the compressed sensing process, the measurement matrix plays a significant role in signal sampling and reconstruction. Therefore, a measurement matrix that is simple in structure, has a small memory, and is easy to implement in hardware is the key to applying compressed sensing theory. Based on the partial Hadamard measurement matrix and a circulating pseudo-random sequence, this paper presents two measurement matrixes that are easy to implement in hardware, namely the sequence partial Hadamard measurement matrix and the recycled pseudo-random sequence measurement matrix. The latter consists of a recycled m sequence and a recycled gold sequence measurement matrix. This further proves that a measurement matrix constructed by a pseudo-random sequence complies with the RIP principle. To test the performance of the two measurement matrixes, a two-dimensional image signal was simulated. It was found that under a low sampling rate, the reconstruction of the sequence partial Hadamard measurement matrix is optimal provided that the length of the sampling signal is 2k. Although reconstruction of the recycled pseudo-random sequence measurement matrix is inferior to the sequence partial Hadamard measurement matrix, it exceeds the Gaussian random measurement matrix, and also overcomes the sequence partial Hadamard measurement matrix’s limitation of a 2k signal length. These two types of measurement matrix are easy to implement in hardware, and avoid the uncertainty and storage waste of a random matrix. Therefore, they are suitable for practical application.
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