Infrared Image Reconstruction Based on Archimedes Spiral Measurement Matrix

doi:10.1007/s12204-018-2011-0

摘要/Abstract

摘要： It is a new research direction to realize infrared (IR) image reconstruction using compressed sensing (CS) theory. In the field of CS, the construction of measurement matrix is very principal. At present, the types of measurement matrices are mainly random and deterministic. The random measurement matrix can well satisfy the property of measurement matrix, but needs a large amount of storage space and has an inconvenient in hardware implementation. Therefore, a deterministic measurement matrix construction method is proposed for IR image reconstruction in this paper. Firstly, a series of points are collected on Archimedes spiral to construct a definite sequence; then the initial measurement matrix is constructed; finally, the deterministic measurement matrix is obtained according to the required sampling rate. Simulation results show that the IR image could be reconstructed by the measured values obtained through the proposed measurement matrix. Moreover, the proposed measurement matrix has better reconstruction performance compared with the Gaussian and Bernoulli random measurement matrices.

关键词: compressed sensing (CS), infrared image reconstruction, deterministic measurement matrices

Abstract: It is a new research direction to realize infrared (IR) image reconstruction using compressed sensing (CS) theory. In the field of CS, the construction of measurement matrix is very principal. At present, the types of measurement matrices are mainly random and deterministic. The random measurement matrix can well satisfy the property of measurement matrix, but needs a large amount of storage space and has an inconvenient in hardware implementation. Therefore, a deterministic measurement matrix construction method is proposed for IR image reconstruction in this paper. Firstly, a series of points are collected on Archimedes spiral to construct a definite sequence; then the initial measurement matrix is constructed; finally, the deterministic measurement matrix is obtained according to the required sampling rate. Simulation results show that the IR image could be reconstructed by the measured values obtained through the proposed measurement matrix. Moreover, the proposed measurement matrix has better reconstruction performance compared with the Gaussian and Bernoulli random measurement matrices.

Key words: compressed sensing (CS), infrared image reconstruction, deterministic measurement matrices

中图分类号:

TN 911.73

JIANG Yilin* (蒋伊琳), WANG Haiyan (王海艳), SHAO Ran (邵然), ZHANG Jianfeng (张建峰). Infrared Image Reconstruction Based on Archimedes Spiral Measurement Matrix[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(2): 204-208.

参考文献 25

[1]	ZHOU M H, CHEN Q. Advances in medical infraredthermal imaging technology [J]. Infrared, 2008, 29(2):38-42 (in Chinese).
[2]	SHAO J, HU W Y, JIA F M, et al. Application of infraredthermal imaging technology to condition-basedmaintenance of power equipment [J]. High Voltage Apparatus,2013, 49(1): 126-129 (in Chinese).
[3]	MARSHALL M V, RASMUSSEN J C, TAN I, et al.Near-infrared fluorescence imaging in humans with indocyaninegreen: A review and update [J]. Open SurgicalOncology Journal, 2010, 2(2): 12-25.
[4]	CANDES E J, TAO T. Decoding by linear programming[J]. IEEE Transactions on Information Theory,2005, 51(12): 4203-4215.
[5]	DONOHO D L. Compressed Sensing [J]. IEEE Transactionson Information Theory, 2006, 52(4): 1289-1306.
[6]	DUARTE M F, DAVENPORT M A, TAKHAR D, etal. Single-pixel imaging via compressive sampling [J].IEEE Signal Processing Magazine, 2008, 25(2): 83-91.
[7]	ZHANG M, BERMAK A. Compressive acquisitionCMOS image sensor: From the algorithm to hardwareimplementation [J]. IEEE Transactions on Very LargeScale Integration (VLSI) Systems, 2010, 18(6): 490-500.
[8]	YANG A Y. GASTPAR M, BAJCSY R, et al. Distributedsensor perception via sparse representation[J]. Proceedings of the IEEE, 2010, 98(9): 1077-1088.
[9]	DAVENPORT M A, WAKIN M B. Analysis of orthogonalmatching pursuit using the restricted isometryproperty [J]. IEEE Transactions on InformationTheory, 2010, 56(9): 4395-4401.
[10]	TSAIG Y, DONOHO D L. Extensions of compressedsensing [J]. Signal Processing, 2006, 86(3): 549-571.
[11]	XIE C J, LIN X, ZHANG T S. Research of image reconstructionof compressed sensing using basis pursuitalgorithm [J]. Electronic Design Engineering, 2011,19(11): 163-166 (in Chinese).
[12]	CHEN S, DONOHO D L, SAUNDERS M A. Atomicdecomposition by basis pursuit [J]. SIAM Journal onScientific Computing, 1998, 20(1): 33-61.
[13]	TROPP J A, GILBERT A C. Signal recovery fromrandom measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory,2007, 53(12): 4655-4666.
[14]	DONOHO D L, TSAIG Y, DRORI I, et al. Sparse solutionof underdetermined systems of linear equationsby stagewise orthogonal matching pursuit [J]. IEEETransactions on Information Theory, 2012, 58(2):1094-1121.
[15]	WANG Q, LI J, SHEN Y. A survey on deterministicmeasurement matrix construction algorithms incompressive sensing [J]. Acta Electronica Sinica, 2013,41(10): 2041-2050 (in Chinese).
[16]	YU Y, PETROPULU A P, POOR H V. Measurementmatrix design for compressive sensing–based MIMOradar [J]. IEEE Transactions on Signal Processing,2011, 59(11): 5338-5352.
[17]	ZHANG G, JIAO S, XU X, et al. Compressed sensingand reconstruction with Bernoulli matrices [C]//IEEEInternational Conference on Information and Automation.Harbin, China: IEEE, 2010: 455-460.
[18]	DEVORE R A. Deterministic constructions of Compressedsensing matrices [J]. Journal of Complexity,2007, 23(4/5/6): 918-925.
[19]	ZHAO R Z, WANG R Q, ZHANG F Z, et al. Researchon the blocked ordered Vandermonde matrixused as measurement matrix for compressed sensing[J]. Journal of Electronics & Information Technology,2015, 37(6): 1317-1322 (in Chinese).
[20]	SUN R, ZHAO H, XU H. The application of improvedHadamard measurement matrix in compressed sensing[C]//International Conference on Systems and Informatics.Yantai, China: IEEE, 2012: 1994-1997.
[21]	YU N Y, LI Y. Deterministic construction of Fourierbasedcompressed sensing matrices using an almostdifference set [J]. EURASIP Journal on Advances inSignal Processing, 2013(1): 1-14.
[22]	BAJWA W U, HAUPT J D, RAZ G M, etal. Toeplitz-structured compressed sensing matrices[C]//Workshop on Statistical Signal Processing. Madison,WI, USA: IEEE, 2007: 294-298.
[23]	YIN W. Practical compressive sensing withToeplitz and circulant matrices [EB/OL]. [2017-11-16]. https://www.researchgate.net/publication/228658617 Practical Compressive Sensing with Toeplitzand Circulant Matrices.
[24]	LU W, LI W, KPALMA K, et al. Compressed sensingperformance of random Bernoulli matrices with highcompression ratio [J]. IEEE Signal Processing Letters,2015, 22(8): 1074-1078.
[25]	SHI G M, LIU D H, GAO D H, et al. Advancesin theory and application of compressed sensing [J].Acta Electronica Sinica, 2009, 37(5): 1070-1081 (inChinese).