基于压缩感知的单像素成像技术研究进展
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摘要
压缩感知作为一种数据采集方式能够突破传统奈奎斯特采样定律的限制,大大减少数据冗余,是一种被应用于众多领域的理论.同时其在信息安全领域的应用也越来越受到重视.介绍了一种利用压缩感知理论搭建的单像素成像系统,从压缩感知基本理论出发,详细阐述了单像素成像技术的基本原理以及实现方法,分析了单像素成像系统在尺寸、精度、速度、成本等方面面临的问题,最后分析了国内外在单像素成像技术方面的研究现状和发展趋势,提出了该技术现有研究的不足之处并给出了未来的研究方向.
Compressive sensing as a data acquisition method breaks through the limitations of the traditional Nyquist sampling law and greatly reduced the data redundancy.It has been applied in many fields so far.At the same time,its application in information security has also been paid more and more attention. This paper introduces a single-pixel imaging system based on compressive sensing theory.From the basic theory of compressed sensing,the basic principle and implementation method of single-pixel imaging technology are described in detail,and the problems faced in different aspects are analyzed.Finally,the domestic and foreign issues are analyzed.In the research status and development trend of single-pixel imaging technology,the inadequacies of the existing research of this technology are proposed and future research directions are given.
Compressive sensing as a data acquisition method breaks through the limitations of the traditional Nyquist sampling law and greatly reduced the data redundancy.It has been applied in many fields so far.At the same time,its application in information security has also been paid more and more attention. This paper introduces a single-pixel imaging system based on compressive sensing theory.From the basic theory of compressed sensing,the basic principle and implementation method of single-pixel imaging technology are described in detail,and the problems faced in different aspects are analyzed.Finally,the domestic and foreign issues are analyzed.In the research status and development trend of single-pixel imaging technology,the inadequacies of the existing research of this technology are proposed and future research directions are given.
引文
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[31]Majumdar A,Ward R K.Compressed sensing of color images[J].Signal Processing,2010,90(12):3122-3127
[32]练秋生,夏长城.基于双树复数小波局部高斯模型的彩色图像压缩感知[J].激光与光电子学进展,2011,48(10):74-81
[33]吕沛,周仁魁,何俊华,等.水下单像素成像系统研究[J].光电子·激光,2011,22(9):1425-1430
[34]Lawrie B J.Pooser R C.Toward real-time quantumimaging with a single pixel camera[J].Optics Express2013,21(6):7549-7559
[35]Sun B,Edgar M P,Bowman R,et al.3Dcomputational imaging with single-pixel detectors[J].Science,2013,340(6134):844-847
[36]Sun M J,Edgar M P,Gibson G M,et al.single-pixel three-dimensional imaging with time-based depth resolution[J].Nature Communications,2016,7:12010
[37]Bi S,Xi N,Lai K W C,et al.Multi-objective optimizing for image recovering in compressive sensing[C]Proc of the 2012IEEE Int Conf on Robotics and Biomimetics.Piscataway,NJ:IEEE,2012:2242-2247
[38]Herman M A,Tidman J,Hewitt D,et al.A higher-speed compressive sensing camera through multi-diode design[C]Proc of the SPIE 8717.Bellingham,WA:SPIE,2013:871706-1-871706-15
[39]彭进业,金浩强,石剑虹,等.高速单像素相机数据采集系统[J].光学精密工程,2014,22(4):837-843
[2]Shannon C E.Communication in the presence of noise[J].Proceedings of the IRE,1949,37(1):10-21
[3]Candès E J.Compressive sampling[J].MartaSanz Solé,2007,17(2):1433-1452
[4]Candès E J,Romberg J.Errata for quantitative robust uncertainty principles and optimally sparse decompositions[J].Foundations of Computational Mathe-Matics,2007,7(4):529-531
[5]Candès E J,Romberg J,Tao T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J].IEEE Trans on Information Theory,2004,52(2):489-509
[6]Candès E J,Romberg J,Tao T.Stable signal recovery from incomplete and inaccurate measurements[J].Communications on Pure and Applied Mathematics,2010,59(8):1207-1223
[7]Donoho D L.Compressed sensing[J].IEEE Trans on Information Theory,2006,52(4):1289-1306
[8]Baraniuk R.Compressive sensing[C]Information Sciences and Systems.Piscataway,NJ:IEEE,2008:4-5
[9]Takhar D,Laska J N,Wakin M B,et al.A new compressive imaging camera architecture using opticaldomaincompression[G]SPIE 6065:The International Society for Optical Engineering.Bellingham,WA:SPIE,2006:43-52
[10]石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081
[11]Baraniuk R,Davenport M,Devore R,et al.A simple proof of the restricted isometry property for random matrices[J].Constructive Approximation,2008,28(3):253-263
[12]Candès E J,Tao T.Decoding by linear programming[J].IEEE Trans on Information Theory,2005,51(12):4203-4215
[13]Mallat S G,Zhang Z.Matching pursuits with timefrequency dictionaries[J].IEEE Trans on Signal Processing,1993,41(12):397-3415
[14]Tropp J,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEETrans on Information Theory,2007,53(12):4655-4666
[15]Donoho D L,Tsaig Y,Drori I,et al.Sparse solution of underdetermined linear equations by stage wise orthogonal matching pursuit[J].IEEE Trans on Information Theory,2012,58(2):1094-1121
[16]Needell D,Vershynin R.Signal recovery from inaccurate and incomplete measurements via regularized orthogonal matching pursuit[J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):310-316
[17]Figueiredo M A,Nowak R D,Wright S J.Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems[J].IEEEJournal of Selected Topics in Signal Processing,2008,1(4):586-597
[18]Daubechies I,Defrise M,De Mol C.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(11):1413-1457
[19]Zayyani H,Babaie-Zadeh M,Jutten C.Bayesian pursuit algorithm for sparse representation[C]Proc of IEEE Int Conf on Acoustics,Speech and Signal Processing.Piscataway,NJ:IEEE,2009:1549-1552
[20]Baron D,Sarvoham R,Baraniuk R G.Bayesian compressive sensing via belief propagation[J].IEEETrans on Signal Processing,2009,58(1):269-280
[21]Seeger M W,Steinke F,Tsuda K.Bayesian inference and optimal design in the sparse linear model[J].Journal of Machine Learning Research Proceedings Track,2007,2(6):444-451
[22]Weiss Y,Chang H S,Freeman W T.Learning compressed sensing[C]Proc of the 45th Allerton Conf on Communications,Control and Computing.New York:Curran Associates,2007:1-7
[23]Gilbert A C,Guha S,Indyk P,et al.Near-optimal sparse Fourier representations via sampling[C]Proc of the 34th Annual ACM Symp on Theory of Computing.New York:ACM,2002:152-161
[24]Gilbert A,Strauss M,Tropp J,Vershynin R.Algorithmic linear dimension reduction in the L1-norm for sparse vectors[C]Proc of the 44th Annual Allerton Conf on Communication,Control and Computing.New York:Curran Associates,2006:1-9
[25]Gormode G,Muthukrishan S.Combinatorial algorithms for compressed sensing[C]Proc of the 40th Annual Conf on Information Sciences and Systems.Piscataway,NJ:IEEE,2006:280-294
[26]Gilbert A,Strauss M,Tropp J,Vershynin R.One sketch for all:Fast algorithms for compressed sensing[C]Proc of the 39th Annual ACM Symp on Theory of Computing.New York:ACM,2007:237-246
[27]Chan W L,Charan K,Takhar D et al.A single-pixel terahertz imaging system based on compressive sensing[J].Applied Physics Letter,2008,93(12):121105
[28]Fu W,Zhu S,Zhang K.Conceptual research on application of single pixel infrared imaging tomissile guidance[C]Proc of Asia-Pacific Conf on Information Processing,Vol 2.Piscataway,NJ:IEEE,2009:185-188
[29]McMackin L,Herman M A,Chatterjee B,et al.A highresolution SWIR camera via compressed sensing[G]SPIE8353:Defense,Security,and Sensing.Bellingham,WA:SPIE,2012:3-10
[30]Nagesh P,Li B.Compressive imaging of color images[C]Proc of IEEE Int Conf on Acoustics,Speech and Signal Processing.Los Alamitos,CA:IEEE Computer Society,2009:1261-1264
[31]Majumdar A,Ward R K.Compressed sensing of color images[J].Signal Processing,2010,90(12):3122-3127
[32]练秋生,夏长城.基于双树复数小波局部高斯模型的彩色图像压缩感知[J].激光与光电子学进展,2011,48(10):74-81
[33]吕沛,周仁魁,何俊华,等.水下单像素成像系统研究[J].光电子·激光,2011,22(9):1425-1430
[34]Lawrie B J.Pooser R C.Toward real-time quantumimaging with a single pixel camera[J].Optics Express2013,21(6):7549-7559
[35]Sun B,Edgar M P,Bowman R,et al.3Dcomputational imaging with single-pixel detectors[J].Science,2013,340(6134):844-847
[36]Sun M J,Edgar M P,Gibson G M,et al.single-pixel three-dimensional imaging with time-based depth resolution[J].Nature Communications,2016,7:12010
[37]Bi S,Xi N,Lai K W C,et al.Multi-objective optimizing for image recovering in compressive sensing[C]Proc of the 2012IEEE Int Conf on Robotics and Biomimetics.Piscataway,NJ:IEEE,2012:2242-2247
[38]Herman M A,Tidman J,Hewitt D,et al.A higher-speed compressive sensing camera through multi-diode design[C]Proc of the SPIE 8717.Bellingham,WA:SPIE,2013:871706-1-871706-15
[39]彭进业,金浩强,石剑虹,等.高速单像素相机数据采集系统[J].光学精密工程,2014,22(4):837-843