模拟信息转换器的实现技术研究
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摘要
在军事通信中，出于安全角度的考虑，往往利用无线电对部队进行调动、部署，现代军事战争中，对电子资源的争夺和利用，甚至能左右一场战争的成败。作为发信方，理所当然的会采取低截获概率的信号体制，如宽频段高速跳频、跳时、猝发等方式。传统的奈奎斯特采样理论要求采样频率至少为信号带宽的两倍，受限于此，对于军事通信中的超宽带高速跳频信号，将产生高采样率、海量数据处理的问题，硬件成本变得昂贵。
奈奎斯特采样理论先通过高速采样得到数字信号，然后对数据进行压缩以滤除冗余数据，这种机制造成了硬件资源的浪费。压缩采样理论突破了传统采样理论的限制，采样过程和压缩过程同时进行，以较低的采样速率，采样得到较少的信息样点，然后通过求解优化问题，便能准确重建原始信号，在许多需要对海量数据进行处理的领域，如超宽带通信、图像处理等，展现了光明的前景。以压缩采样理论为基础的模拟信息转换器(AIC)使得压缩采样理论真正进入实用，它可以代替传统的ADC，以较低的速率对高速模拟信号进行实时采样，获取所关心的信息，有效解决了传统采样理论遇到的瓶颈。AIC要求具有实时性，及时对高速信号进行感知，同时要求系统具有较强的乘法运算能力，以完成高维的矩阵相乘，这就使得硬件实现变得困难。
本文内容主要包括三部分：第一部分介绍压缩采样理论的基本原理，为后期介绍的AIC提供理论基础，对基于稀疏分解的重建算法(BP算法、OMP算法和StOMP算法)进行了性能仿真，找到每种算法的优势和不足；第二部分介绍了三种AIC的实现结构：预调制型AIC、直接型AIC、分段型AIC，通过性能仿真比较三种AIC的性能、特点；第三部分针对预调制型AIC提出了硬件实现方案，利用register-to-register模型定量分析了该电路所能跑的最高时钟频率，详细分析了各个子系统可能引入的噪声及对整个系统的影响，同时给出了OMP重建算法的一种硬件电路框图，通过矩阵变换，巧妙的避开了平方根的求解问题，降低了硬件电路的复杂度。
For security reasons,ratio is often used to command or deploy the army in the militarycommunications. It is important to the electric source, sometimes it even can affect the result of themodern warfare. Of course,the sender will chose a safe way,such as Ultra-Wideband signal,Hopsignal and burst signal,to avoid of being tapped. By the traditional Nyquist theory,the sample rateshould be at least two times of the signal bandwidth, then in terms of Ultra-Wideband hop signal, itis hard to sample and treat the mass sample data.
Sample the signal first to get the digital signal and then compress it to filter the redundant databy the Nyquist theory. It is waste for hardware source.Compressive Sampling(CS) theory can breakthe restriction of the Nyquist theory by sample and compress the signal at the same time.It samplesat low rate,gets less information data in CS.The original signal will be reconstructed by solving aoptimization problem.CS is widely used in Ultra-Wideband communication field and imagepricessing field. The Analog to Information Converter(AIC) which based on CS makes CSpractical.AIC can replace the traditional ADC to sample the high rate analog signal at lower rate andget the information we want. With the information we sense,we can reconstruct the analog signal,avioding the bottleneck of the traditional Nyquist theory. It is used to sense the high-frequencyanalog signal,so the AIC must be real-time. It also should be good at multiplication to complete thematrix multiplication.
There are three parts in this paper. The first part is basic. In this part , the fundamentals of CS isintroduced. We must get it before we study the AIC. We also sim with the restruction algorithmbased on the sparse decompression.,including BP,OMP,StOMP.The superiority and Insufficient ofeach algorithm is get. In second part ,we introduce three AICs,including modulation AIC,parallelAIC and segmented AIC. The performance and characteristic of each type of AIC is get from thesimulation. The third part is the main part. A hardware implemention for the modulation AIC isproposed. The maximum frequency is obtain with the register-to-register mode. And then we analyzethe influence to the hardware system of the interference, because each sub-system will lead into theinterference inevitable. At last we propose a hardware circuit diagram to the OMP restructionalgorithm.It avoids square roots with the clever matrix transform.With this program,the complexityof the circuit is cut down significant.
奈奎斯特采样理论先通过高速采样得到数字信号，然后对数据进行压缩以滤除冗余数据，这种机制造成了硬件资源的浪费。压缩采样理论突破了传统采样理论的限制，采样过程和压缩过程同时进行，以较低的采样速率，采样得到较少的信息样点，然后通过求解优化问题，便能准确重建原始信号，在许多需要对海量数据进行处理的领域，如超宽带通信、图像处理等，展现了光明的前景。以压缩采样理论为基础的模拟信息转换器(AIC)使得压缩采样理论真正进入实用，它可以代替传统的ADC，以较低的速率对高速模拟信号进行实时采样，获取所关心的信息，有效解决了传统采样理论遇到的瓶颈。AIC要求具有实时性，及时对高速信号进行感知，同时要求系统具有较强的乘法运算能力，以完成高维的矩阵相乘，这就使得硬件实现变得困难。
本文内容主要包括三部分：第一部分介绍压缩采样理论的基本原理，为后期介绍的AIC提供理论基础，对基于稀疏分解的重建算法(BP算法、OMP算法和StOMP算法)进行了性能仿真，找到每种算法的优势和不足；第二部分介绍了三种AIC的实现结构：预调制型AIC、直接型AIC、分段型AIC，通过性能仿真比较三种AIC的性能、特点；第三部分针对预调制型AIC提出了硬件实现方案，利用register-to-register模型定量分析了该电路所能跑的最高时钟频率，详细分析了各个子系统可能引入的噪声及对整个系统的影响，同时给出了OMP重建算法的一种硬件电路框图，通过矩阵变换，巧妙的避开了平方根的求解问题，降低了硬件电路的复杂度。
For security reasons,ratio is often used to command or deploy the army in the militarycommunications. It is important to the electric source, sometimes it even can affect the result of themodern warfare. Of course,the sender will chose a safe way,such as Ultra-Wideband signal,Hopsignal and burst signal,to avoid of being tapped. By the traditional Nyquist theory,the sample rateshould be at least two times of the signal bandwidth, then in terms of Ultra-Wideband hop signal, itis hard to sample and treat the mass sample data.
Sample the signal first to get the digital signal and then compress it to filter the redundant databy the Nyquist theory. It is waste for hardware source.Compressive Sampling(CS) theory can breakthe restriction of the Nyquist theory by sample and compress the signal at the same time.It samplesat low rate,gets less information data in CS.The original signal will be reconstructed by solving aoptimization problem.CS is widely used in Ultra-Wideband communication field and imagepricessing field. The Analog to Information Converter(AIC) which based on CS makes CSpractical.AIC can replace the traditional ADC to sample the high rate analog signal at lower rate andget the information we want. With the information we sense,we can reconstruct the analog signal,avioding the bottleneck of the traditional Nyquist theory. It is used to sense the high-frequencyanalog signal,so the AIC must be real-time. It also should be good at multiplication to complete thematrix multiplication.
There are three parts in this paper. The first part is basic. In this part , the fundamentals of CS isintroduced. We must get it before we study the AIC. We also sim with the restruction algorithmbased on the sparse decompression.,including BP,OMP,StOMP.The superiority and Insufficient ofeach algorithm is get. In second part ,we introduce three AICs,including modulation AIC,parallelAIC and segmented AIC. The performance and characteristic of each type of AIC is get from thesimulation. The third part is the main part. A hardware implemention for the modulation AIC isproposed. The maximum frequency is obtain with the register-to-register mode. And then we analyzethe influence to the hardware system of the interference, because each sub-system will lead into theinterference inevitable. At last we propose a hardware circuit diagram to the OMP restructionalgorithm.It avoids square roots with the clever matrix transform.With this program,the complexityof the circuit is cut down significant.
引文
[1]初仁辛,孙圣和.非均匀采样信号理论及其发展[J].电子商务,1997,(07).
[2] LCAV, Swiss Fed. Inst. of Technol., Lausanne. Sampling signals with finite rate of innovation[J]. IEEE Transactions on Signal Processing,2002,50(6):1417-1428.
[3] Sanjoy Dasgupta, Anupam Gupta. An elementary proof of a theorem of Johnson and Lindenstrauss[J]. Random Structures & Algorithms,2003,22(1):60-65
[4]裴进凯.低截获概率雷达信号分析与检测[D].西安：西安电子科技大学硕士学位论文，2009:01-04.
[5]李英祥.低截获概率信号非平稳处理技术研究[D].成都：电子科技大学硕士学位论文，2002:01-12.
[6]刘姜玲，王小谟,，陈捷.一种具有低截获概率的新型阵列天线[C].成都：2009年全国天线年会，2009:402-405
[7]陈知明.低截获概率技术在机载火控雷达中的应用[D].南京：南京理工大学硕士学位论文，2008:10-09.
[8]岳海啸.高速跳频通信系统关键技术研究与基带设计[D].西安：西北工业大学硕士学位论文，2006:03-05.
[9]蒋定顺,，金力军.高速跳频通信系统同步技术研究[J].电子科技大学学报, 2005，34(1)：48-52.
[10]彭伟夫.短波高速跳频系统的同步捕获技术[D].成都：电子科技大学硕士学位论文，2009:5-20.
[11]岳峰巍.跳频通信网台分选方法的研究与仿真实现[D].成都：电子科技大学硕士学位论文，2010:5-01.
[12] B. Kashin. The widths of certain finite dimensional sets and classes of smooth functions. Izv Akad Nauk SSSR.1977, 41(2): 334-351.
[13] M. Duarte, M. Davenport, D. Takbar, etc. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 2008, 25(2): 82-91.
[14] R. Baraniuk, P. Steeghs, Compressive radar imaging. IEEE Radar Conference, Waltham,Massachusetts, April2007.
[15] M. Lustig, D. L. Donoho, J. M. Pauly. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine. 2007, 58(6): 1182-1195.
[16] M. Sheikh, O. Milenkovic, R. Baraniuk. Designing compressive sensing DNA microarrays. IEEE Workshop on Computational Advances in Multi-Sensor Adaptive Processing（CAMSAP）, St. Thomas, U.S. Virgin Islands, December 2007.
[17] P. Borgnat, P. Flandrin. Time-frequency localization from sparsity constraints. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing（ICASSP）. Piscataway: Institute of Electrical and Electronics Engineers Inc.,2008: 3785-3788.
[18] R. Willett, M. Gehm, D. Brady. Multiscale reconstruction for computational spectral imaging. Proceedings ofSPIE-IS and T Electronic Imaging-Computational Imaging. Bellingham: SPIE, 2007, 64980L.
[19] W. Bajwa, J. Haupt, A. Sayeed, etc. Compressive wireless sensing. Int. Conf. on Information Processing in Sensor Networks (IPSN), Nashville, Tennessee, 2006: 134-142.
[20] J. Bobin, J. Starck, R. Ottensamer. Compressed sensing in astronomy. Applied Mathematics and Computation,2008, 206 (2): 980-988
[21] D. H. Liu, G. M. Shi, D. H. Gao. A new method for signal sparse decomposition, ISPACS'07, Xiamen, China,2007: 45-48.
[22] Y. Zhang, S. Mei, Q. Chen, et al. A novel image/video coding method based on compressed sensing theory. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008: 1361-1364.
[23]尹忠科,解梅,王建英.基于稀疏分解的图像去噪.电子科技大学学报, 2006, 35(6):876-878.
[24]傅霆,尧德中.稀疏分解的加权迭代方法及其初步应用.电子学报, 2004, 32(4):567-570.
[25]杜小勇.稀疏成份分析及在雷达成像处理中的应用[博士学位论文].国防科技大学,2005.
[26] F. Bergeaud and S. Mallat. Matching pursuit of images. In Proc. International Conference on Image Processing,1995, 1: 53-56.
[27] M. Goodwin and M. Vetterli. Atomic decompositions of audio signals. Proceedings of Workshop on Applications of Signal Processing to Audio and Acoustics, New York, 1997:4-7.
[28] R. Neff and A. Zakhor. Very low bit rate video coding based on matching Pursuits. IEEE Trans. Circuits Syst. Video Technol. Feb. 1997, 7: 158-171.
[29] D. L. Donoho.De-Noising by Soft-Thresholding. IEEE Transactions on Information.Theory,1995, 41(3):613-627.
[30]韦泉华.基于稀疏表示的盲信号分离算法及其改进[硕士学位论文].中国地质大学,2006.
[31] A. Shmilovici, O. Maimon. Application of adaptive matching pursuit to adaptive control of nonlinear dynamic systems. IEEE Proceeding of Control Theory and Application, 1998, 145(6):575-582.
[32] F. P. Kourouniotis, R. F. Kubichek, N. Boyd. Application of the wave transform and matching pursuit algorithm in seismic data processing for the development of new noise reduction technique. Int. Symposium on Optimal Sci. Eng. And Instrumentation, Dever, CO, August, 1996.
[33] E. L. Pennec, S Mallat. Image compression with geometrical wavelets. Proceedings of IEEE Conference on Image Processing (ICIP’00). Vancouver, Canada, 2000, 1: 661-664.
[34] Candes E.J, Tao T. Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies[J] IEEE Transactions on Information Theory, 2006,51(12): 5406-5425.
[35] Wei Lu, Vaswani, N. Modified Basis Pursuit Denoising(modified-BPDN) for noisy compressive sensing with partially known support [C] 2010 IEEE International Conference on Acoustics Speech and Signal Processing.2010: 3926-3929.
[36] Boufounos, P.T.，Baraniuk, 1-Bit compressive sensing[A]. R.G.. CISS 2008. 42nd Annual Conference on Information Sciences and Systems, 2008[C]. Princeton, NJ:2008:16-21.
[37] Lihan He，Haojun Chen，Carin, L. Tree-Structured Compressive Sensing With Variational Bayesian Analysis[J]. IEEE Signal Processing Letters,2010,17(3):233-236.
[38]初仁辛,孙圣和.非均匀采样信号理论及其发展[J].电子商务,1997,(07).
[39] LCAV, Swiss Fed. Inst. of Technol., Lausanne. Sampling signals with finite rate of innovation[J]. IEEE Transactions on Signal Processing,2002,50(6):1417-1428.
[40] Olshausen B, Field D. Sparse coding with an overcomplete basis set: A strategy employed by V1?[J]. Vision Research,1997,37:3311-3325.
[41] Jean-Luc Starck, Candes, E.J., Donoho, D.L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing,2002,11(6):670-684.
[42]王建英，尹忠科，张春梅.信号与图像的稀疏分解及初步应用[M].成都：西南交通大学出版社，2006.
[43] Baraniuk, R. Compressive sensing[C]. 42nd Annual Conference on Information Sciences and Systems, Houston, 2008, 29:19-21.
[44] Emmanuel J. Candes. The restricted isometry property and its implications for compressed sensing[J]. Theory of Signals/Mathematical Analysis, 2008,346(9-10): 589-592.
[45] Candes, Emmanuel J, Tao Terence. Decoding by linear programming[J]. IEEE Transactions on Information Theory, 2005,51(12):4203-4215.
[46] Candes E.J,Wakin, M.B. An Introduction To Compressive Sampling [J]. IEEE Signal Processing Magazine,2008,25(2): 21-30.
[47] R.Baraniuk. A lecture on Compressive Sensing. IEEE Signal Processing Magazine,2007,24(4):118-121
[48] Baraniuk R.G, Cevher V, Duarte M.F et al. Model-based compressive sensing[J]. IEEE Transactions on Information Theory, 2010,56(4):1982-2001.
[49] J.A Tropp,A Gilbert Signal Recovery from Partial Information by Orthogonal Matching Pusrsuit. IEEE Trans on Information Theory,2007,53(12):4655-4666.
[50] L. M. Bregman. The method of successive projection for finding a common point of convex sets. Doklady Mathematics, 1965, 6: 688-692.
[51] C. La, M. N. Do. Signal reconstruction using sparse tree representation. Proceedings of SPIE. San Diego, CA, United States: International Society for Optical Engineering. 2005, 5914: 1-11.
[52] D. Needell, R. Vershynin. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. http://www.math.ucdavis.edu/%7Evershynin/ papers/ROMP-stability.pdf.
[53] D. Needell, R. Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. http://www.math.ucdavis.edu/~vershynin/papers/ROMP. pdf.
[54] S. J. Kim, K. Koh, M. Lustig, et al. A method for large-scale 1 l -regularized least-squares. IEEE Journal on Selected Topics in Signal Processing, 2007, 4(1): 606-617.
[55] S. Chen and D. Donoho. Basis Pursuit. TechnicalReport, Department of Statistics, Stanford University.
[56] Mallat S,Zhang Z..Matching pursuit with time-frequency dictionaries [J]. IEEE Trans. On SignalProcessing,1933,41,(12):3397-3415
[57] D.L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (StOMP), submitted for publication.
[58] Saini Kirolos, Tamer Ragheb. Practical Issues in Implementing Analog-to-Information Converters[J]. The 6th International Workshop on System-on-Chip for Real-Time Applications,2006:141-146.
[59] Jason Laska,Sami Kirolos,Yehia Massoud. Random Sampling for Analog-to-Information Conversion of Wideband Signals[J]. 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.2006:119-122.
[60] Z. Yu, S. Hoyos, and B. M. Sadler,“Mixed-signal parallel compressed sensing and reception for cognitive radio,”in Proc. IEEE ICASSP, Las Vegas, USA, Apr. 2008, pp. 3861–3864.
[61] Omid Taheri, Sergiy A. Vorobyov. Segmented Compressed Sampling for Analog-to-Information Conversion:Method and Performance Analysis[J]. IEEE Transactions on Signal Processing.2011,59(2):554-572.
[62] R. Baraniuk, M. Davenport, R. De Vore, and M. Wakin,“A simple proof of the restricted isometry property for random matrices,”ConstructiveApproximation, vol. 28, pp. 253–263, Dec. 2008.
[63] Omid Taheri, Sergiy A. Vorobyov. Segmented Compressed Sampling for Analog-to-Information Conversion[J]. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).2009:113-116.
[64] V. Stojanovic and V. G. Oklobdzija, "Comparative Analysis of Master-Slave Latches and Flip-Flops for High-Performance and Low-Power Systems" IEEE JOURNAL OF SOLID-STATE CIRCUITS, 1999.
[65] Kirolos S, Ragheb T, Laska J. Practical Issues in Implementing Analog-to-Information Converters [C]. The6th International Workshop on System-on-Chip for Real-Time Applications, Cairo,Egypt 2006: 141-146.
[66]董在望，李冬梅等.高等模拟集成电路(M).北京：清华大学出版社，2006. 55.
[67] R.C.Yen and P.R. Gray "An MOS switched-capacitor instrumentation amplifier," IEEE J.Solid-state Circuits, vol. SC-17, pp. 1008-1013, Dec. 1982.
[68] K. Watanabe and S . Ogawa, "Clock-feedthrough compensated samplehold circuits," Electronic Letters, vol.24, No. 19, pp.1226-1228, Sept. 15, 1988.
[69] Minkyu Song. A Clock Feedthrough Reduction Circuit for Switched-Current Systems[J]. IEEE Journal of Solid-State Circuits.1993,28(2):133-137.
[70]黄智伟.混频器电路设计(M).西安：西安电子科技大学出版社，2009.1-18.
[71] J. Tropp and A. Gilbert,“Signal recovery from random measurements via orthogonal matching pursuit,”IEEE Trans. on Information Theory,vol. 53, no. 12, pp. 4655–4666, 2007.
[72] Avi Septimus,Raphael Steinberg. Compressive Sampling Hardware Reconstruction[J]. Proceedings of 2010 IEEE International Symposium on Circuits and Systems (ISCAS).2010, 3316–3319.
[73]朱世宇，夏汝华等.基于FPGA的阵列乘法器的设计与实现[J].自动化与仪器仪表，2011，(4)：60-61.
[2] LCAV, Swiss Fed. Inst. of Technol., Lausanne. Sampling signals with finite rate of innovation[J]. IEEE Transactions on Signal Processing,2002,50(6):1417-1428.
[3] Sanjoy Dasgupta, Anupam Gupta. An elementary proof of a theorem of Johnson and Lindenstrauss[J]. Random Structures & Algorithms,2003,22(1):60-65
[4]裴进凯.低截获概率雷达信号分析与检测[D].西安：西安电子科技大学硕士学位论文，2009:01-04.
[5]李英祥.低截获概率信号非平稳处理技术研究[D].成都：电子科技大学硕士学位论文，2002:01-12.
[6]刘姜玲，王小谟,，陈捷.一种具有低截获概率的新型阵列天线[C].成都：2009年全国天线年会，2009:402-405
[7]陈知明.低截获概率技术在机载火控雷达中的应用[D].南京：南京理工大学硕士学位论文，2008:10-09.
[8]岳海啸.高速跳频通信系统关键技术研究与基带设计[D].西安：西北工业大学硕士学位论文，2006:03-05.
[9]蒋定顺,，金力军.高速跳频通信系统同步技术研究[J].电子科技大学学报, 2005，34(1)：48-52.
[10]彭伟夫.短波高速跳频系统的同步捕获技术[D].成都：电子科技大学硕士学位论文，2009:5-20.
[11]岳峰巍.跳频通信网台分选方法的研究与仿真实现[D].成都：电子科技大学硕士学位论文，2010:5-01.
[12] B. Kashin. The widths of certain finite dimensional sets and classes of smooth functions. Izv Akad Nauk SSSR.1977, 41(2): 334-351.
[13] M. Duarte, M. Davenport, D. Takbar, etc. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 2008, 25(2): 82-91.
[14] R. Baraniuk, P. Steeghs, Compressive radar imaging. IEEE Radar Conference, Waltham,Massachusetts, April2007.
[15] M. Lustig, D. L. Donoho, J. M. Pauly. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine. 2007, 58(6): 1182-1195.
[16] M. Sheikh, O. Milenkovic, R. Baraniuk. Designing compressive sensing DNA microarrays. IEEE Workshop on Computational Advances in Multi-Sensor Adaptive Processing（CAMSAP）, St. Thomas, U.S. Virgin Islands, December 2007.
[17] P. Borgnat, P. Flandrin. Time-frequency localization from sparsity constraints. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing（ICASSP）. Piscataway: Institute of Electrical and Electronics Engineers Inc.,2008: 3785-3788.
[18] R. Willett, M. Gehm, D. Brady. Multiscale reconstruction for computational spectral imaging. Proceedings ofSPIE-IS and T Electronic Imaging-Computational Imaging. Bellingham: SPIE, 2007, 64980L.
[19] W. Bajwa, J. Haupt, A. Sayeed, etc. Compressive wireless sensing. Int. Conf. on Information Processing in Sensor Networks (IPSN), Nashville, Tennessee, 2006: 134-142.
[20] J. Bobin, J. Starck, R. Ottensamer. Compressed sensing in astronomy. Applied Mathematics and Computation,2008, 206 (2): 980-988
[21] D. H. Liu, G. M. Shi, D. H. Gao. A new method for signal sparse decomposition, ISPACS'07, Xiamen, China,2007: 45-48.
[22] Y. Zhang, S. Mei, Q. Chen, et al. A novel image/video coding method based on compressed sensing theory. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008: 1361-1364.
[23]尹忠科,解梅,王建英.基于稀疏分解的图像去噪.电子科技大学学报, 2006, 35(6):876-878.
[24]傅霆,尧德中.稀疏分解的加权迭代方法及其初步应用.电子学报, 2004, 32(4):567-570.
[25]杜小勇.稀疏成份分析及在雷达成像处理中的应用[博士学位论文].国防科技大学,2005.
[26] F. Bergeaud and S. Mallat. Matching pursuit of images. In Proc. International Conference on Image Processing,1995, 1: 53-56.
[27] M. Goodwin and M. Vetterli. Atomic decompositions of audio signals. Proceedings of Workshop on Applications of Signal Processing to Audio and Acoustics, New York, 1997:4-7.
[28] R. Neff and A. Zakhor. Very low bit rate video coding based on matching Pursuits. IEEE Trans. Circuits Syst. Video Technol. Feb. 1997, 7: 158-171.
[29] D. L. Donoho.De-Noising by Soft-Thresholding. IEEE Transactions on Information.Theory,1995, 41(3):613-627.
[30]韦泉华.基于稀疏表示的盲信号分离算法及其改进[硕士学位论文].中国地质大学,2006.
[31] A. Shmilovici, O. Maimon. Application of adaptive matching pursuit to adaptive control of nonlinear dynamic systems. IEEE Proceeding of Control Theory and Application, 1998, 145(6):575-582.
[32] F. P. Kourouniotis, R. F. Kubichek, N. Boyd. Application of the wave transform and matching pursuit algorithm in seismic data processing for the development of new noise reduction technique. Int. Symposium on Optimal Sci. Eng. And Instrumentation, Dever, CO, August, 1996.
[33] E. L. Pennec, S Mallat. Image compression with geometrical wavelets. Proceedings of IEEE Conference on Image Processing (ICIP’00). Vancouver, Canada, 2000, 1: 661-664.
[34] Candes E.J, Tao T. Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies[J] IEEE Transactions on Information Theory, 2006,51(12): 5406-5425.
[35] Wei Lu, Vaswani, N. Modified Basis Pursuit Denoising(modified-BPDN) for noisy compressive sensing with partially known support [C] 2010 IEEE International Conference on Acoustics Speech and Signal Processing.2010: 3926-3929.
[36] Boufounos, P.T.，Baraniuk, 1-Bit compressive sensing[A]. R.G.. CISS 2008. 42nd Annual Conference on Information Sciences and Systems, 2008[C]. Princeton, NJ:2008:16-21.
[37] Lihan He，Haojun Chen，Carin, L. Tree-Structured Compressive Sensing With Variational Bayesian Analysis[J]. IEEE Signal Processing Letters,2010,17(3):233-236.
[38]初仁辛,孙圣和.非均匀采样信号理论及其发展[J].电子商务,1997,(07).
[39] LCAV, Swiss Fed. Inst. of Technol., Lausanne. Sampling signals with finite rate of innovation[J]. IEEE Transactions on Signal Processing,2002,50(6):1417-1428.
[40] Olshausen B, Field D. Sparse coding with an overcomplete basis set: A strategy employed by V1?[J]. Vision Research,1997,37:3311-3325.
[41] Jean-Luc Starck, Candes, E.J., Donoho, D.L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing,2002,11(6):670-684.
[42]王建英，尹忠科，张春梅.信号与图像的稀疏分解及初步应用[M].成都：西南交通大学出版社，2006.
[43] Baraniuk, R. Compressive sensing[C]. 42nd Annual Conference on Information Sciences and Systems, Houston, 2008, 29:19-21.
[44] Emmanuel J. Candes. The restricted isometry property and its implications for compressed sensing[J]. Theory of Signals/Mathematical Analysis, 2008,346(9-10): 589-592.
[45] Candes, Emmanuel J, Tao Terence. Decoding by linear programming[J]. IEEE Transactions on Information Theory, 2005,51(12):4203-4215.
[46] Candes E.J,Wakin, M.B. An Introduction To Compressive Sampling [J]. IEEE Signal Processing Magazine,2008,25(2): 21-30.
[47] R.Baraniuk. A lecture on Compressive Sensing. IEEE Signal Processing Magazine,2007,24(4):118-121
[48] Baraniuk R.G, Cevher V, Duarte M.F et al. Model-based compressive sensing[J]. IEEE Transactions on Information Theory, 2010,56(4):1982-2001.
[49] J.A Tropp,A Gilbert Signal Recovery from Partial Information by Orthogonal Matching Pusrsuit. IEEE Trans on Information Theory,2007,53(12):4655-4666.
[50] L. M. Bregman. The method of successive projection for finding a common point of convex sets. Doklady Mathematics, 1965, 6: 688-692.
[51] C. La, M. N. Do. Signal reconstruction using sparse tree representation. Proceedings of SPIE. San Diego, CA, United States: International Society for Optical Engineering. 2005, 5914: 1-11.
[52] D. Needell, R. Vershynin. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. http://www.math.ucdavis.edu/%7Evershynin/ papers/ROMP-stability.pdf.
[53] D. Needell, R. Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. http://www.math.ucdavis.edu/~vershynin/papers/ROMP. pdf.
[54] S. J. Kim, K. Koh, M. Lustig, et al. A method for large-scale 1 l -regularized least-squares. IEEE Journal on Selected Topics in Signal Processing, 2007, 4(1): 606-617.
[55] S. Chen and D. Donoho. Basis Pursuit. TechnicalReport, Department of Statistics, Stanford University.
[56] Mallat S,Zhang Z..Matching pursuit with time-frequency dictionaries [J]. IEEE Trans. On SignalProcessing,1933,41,(12):3397-3415
[57] D.L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (StOMP), submitted for publication.
[58] Saini Kirolos, Tamer Ragheb. Practical Issues in Implementing Analog-to-Information Converters[J]. The 6th International Workshop on System-on-Chip for Real-Time Applications,2006:141-146.
[59] Jason Laska,Sami Kirolos,Yehia Massoud. Random Sampling for Analog-to-Information Conversion of Wideband Signals[J]. 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.2006:119-122.
[60] Z. Yu, S. Hoyos, and B. M. Sadler,“Mixed-signal parallel compressed sensing and reception for cognitive radio,”in Proc. IEEE ICASSP, Las Vegas, USA, Apr. 2008, pp. 3861–3864.
[61] Omid Taheri, Sergiy A. Vorobyov. Segmented Compressed Sampling for Analog-to-Information Conversion:Method and Performance Analysis[J]. IEEE Transactions on Signal Processing.2011,59(2):554-572.
[62] R. Baraniuk, M. Davenport, R. De Vore, and M. Wakin,“A simple proof of the restricted isometry property for random matrices,”ConstructiveApproximation, vol. 28, pp. 253–263, Dec. 2008.
[63] Omid Taheri, Sergiy A. Vorobyov. Segmented Compressed Sampling for Analog-to-Information Conversion[J]. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).2009:113-116.
[64] V. Stojanovic and V. G. Oklobdzija, "Comparative Analysis of Master-Slave Latches and Flip-Flops for High-Performance and Low-Power Systems" IEEE JOURNAL OF SOLID-STATE CIRCUITS, 1999.
[65] Kirolos S, Ragheb T, Laska J. Practical Issues in Implementing Analog-to-Information Converters [C]. The6th International Workshop on System-on-Chip for Real-Time Applications, Cairo,Egypt 2006: 141-146.
[66]董在望，李冬梅等.高等模拟集成电路(M).北京：清华大学出版社，2006. 55.
[67] R.C.Yen and P.R. Gray "An MOS switched-capacitor instrumentation amplifier," IEEE J.Solid-state Circuits, vol. SC-17, pp. 1008-1013, Dec. 1982.
[68] K. Watanabe and S . Ogawa, "Clock-feedthrough compensated samplehold circuits," Electronic Letters, vol.24, No. 19, pp.1226-1228, Sept. 15, 1988.
[69] Minkyu Song. A Clock Feedthrough Reduction Circuit for Switched-Current Systems[J]. IEEE Journal of Solid-State Circuits.1993,28(2):133-137.
[70]黄智伟.混频器电路设计(M).西安：西安电子科技大学出版社，2009.1-18.
[71] J. Tropp and A. Gilbert,“Signal recovery from random measurements via orthogonal matching pursuit,”IEEE Trans. on Information Theory,vol. 53, no. 12, pp. 4655–4666, 2007.
[72] Avi Septimus,Raphael Steinberg. Compressive Sampling Hardware Reconstruction[J]. Proceedings of 2010 IEEE International Symposium on Circuits and Systems (ISCAS).2010, 3316–3319.
[73]朱世宇，夏汝华等.基于FPGA的阵列乘法器的设计与实现[J].自动化与仪器仪表，2011，(4)：60-61.