基于IR-UWB信号的LSM成像算法的研究
摘要
随着人们对于信息量的需求迅猛的增长,信息获取的方式也出现较大的变化,由原来的接触式向非接触式发展。从原来单纯的各种物理量等数据的采集,逐步发展到利用电磁信号本身来实现对周围环境的感知。由于IR-UWB(Impulse Radio Ultra Wideband)在获取和承载信息方面具有很多优势,所以针对各种应用背景的基于IR-UWB技术的研究也拓展开来,在成像技术方面显得尤为突出。
电磁散射是一种物理现象,在非均匀场的前提下,入射波被散射后,空间中各点的总场可以表示为原来的入射场和散射后形成的散射场共同作用的结果。
当散射体的几何和物理特性已知时,电磁散射正问题就是确定散射域的问题。然而,逆散射问题是从远场模式的信息推断出非均匀场的信息。也就是说:散射波的采集在距散射体很远的位置完成。古典的电磁逆散射理论提出了大量的具有挑战性的数学问题。首先,这是由于在试图建立求解过程中,对散射体的发生的物理条件的不确定性所决定的。其次,用Hadamard的话来说,几乎所有的逆散射问题尤其是有重要应用意义的,都存在所谓的不适应问题。因此,要想得到可靠的近似解,必须面对(在某一阶段)解的唯一性和数值稳定性。利用UWB信号成像可以获得高质量的解。但是,采用宽带或者超宽带激励信号的成像算法(收发分置的或者收发同置的)通常涉及到动态特性。特别值得关注的是,任何的解决逆散射问题的方法都必须(在某一阶段)引入一定的正则化过程,以便消除由不适应问题产生的虚假波动,这一点是毋庸置疑的。
本文介绍了两种基于IR-UWB信号的成像算法:DAS(时延求和算法)和LSM(线性采样算法)。并在此基础上提出了修正的线性采样算法(MSM),以及成功地使用Morozov's离散原理选择最优正则化参数α。
Along with the rushing grow up of the people’s need for information, the way and method of we get the information is not as usual when we use touching; now we use non-touching, i.e. we got the information form the data such as physical properties before, but now we get it form the electromagnetic signal itself which apperceives the ambience. Researches on many applications which base on IR-UWB (Impulse Radio Ultra Wideband) has been developed due to IR-UWB has great superiority on the information capture and carrier, from which the imaging technology stands out.
Electromagnetic scattering is a kind of physical phenomenon, in the presence of an in-homogeneity, an electromagnetic incident wave is scattered and the total field at any point in space can be written as the sum of the original incident field and the scattered field.
The electromagnetic direct scattering problems are the problem of determining the scattered field when the geometrical and physical properties of the scatter are known. The inverse scattering problem is the problem of inferring information on the in-homogeneity from knowledge of the far-field pattern, i.e. the scattered wave at large distances from the scatter. Classical electromagnetic inverse scattering theory provides a rich supply of challenging mathematical problems. First of all, this is due to the fact that the unknown physical conditions where the scattering takes place create difficulties in trying to construct the solution procedure. Second, all the inverse scattering problems significant in applications belong to the class of so-called ill-posed problems in the sense of Hadamard and therefore any reliable approach to their solution must face, at some stage, questions of uniqueness and numerical stability. Using the UWB signal imagery, may obtain the higher solution. Imaging methods (bistatic or monostatic) base on broadband or UWB stimulation signals are usually referred to as migrations.In particular, it is well established that any numerical implementation of a method for the solution of an inverse scattering problem must, at some step, incorporate a regularization procedure in order to eliminate the artificial oscillations due to the ill-posed of the problem.
In this paper, introduce two kinds of method base on IR-UWB: DAS (Delay-And-Sum) and LSM (Linear Sampling Method).Then introduce a modifying method of LSM (MSM). Moreover, we use the Morozov's discrete principle to choice the parameter of regularization.
电磁散射是一种物理现象,在非均匀场的前提下,入射波被散射后,空间中各点的总场可以表示为原来的入射场和散射后形成的散射场共同作用的结果。
当散射体的几何和物理特性已知时,电磁散射正问题就是确定散射域的问题。然而,逆散射问题是从远场模式的信息推断出非均匀场的信息。也就是说:散射波的采集在距散射体很远的位置完成。古典的电磁逆散射理论提出了大量的具有挑战性的数学问题。首先,这是由于在试图建立求解过程中,对散射体的发生的物理条件的不确定性所决定的。其次,用Hadamard的话来说,几乎所有的逆散射问题尤其是有重要应用意义的,都存在所谓的不适应问题。因此,要想得到可靠的近似解,必须面对(在某一阶段)解的唯一性和数值稳定性。利用UWB信号成像可以获得高质量的解。但是,采用宽带或者超宽带激励信号的成像算法(收发分置的或者收发同置的)通常涉及到动态特性。特别值得关注的是,任何的解决逆散射问题的方法都必须(在某一阶段)引入一定的正则化过程,以便消除由不适应问题产生的虚假波动,这一点是毋庸置疑的。
本文介绍了两种基于IR-UWB信号的成像算法:DAS(时延求和算法)和LSM(线性采样算法)。并在此基础上提出了修正的线性采样算法(MSM),以及成功地使用Morozov's离散原理选择最优正则化参数α。
Along with the rushing grow up of the people’s need for information, the way and method of we get the information is not as usual when we use touching; now we use non-touching, i.e. we got the information form the data such as physical properties before, but now we get it form the electromagnetic signal itself which apperceives the ambience. Researches on many applications which base on IR-UWB (Impulse Radio Ultra Wideband) has been developed due to IR-UWB has great superiority on the information capture and carrier, from which the imaging technology stands out.
Electromagnetic scattering is a kind of physical phenomenon, in the presence of an in-homogeneity, an electromagnetic incident wave is scattered and the total field at any point in space can be written as the sum of the original incident field and the scattered field.
The electromagnetic direct scattering problems are the problem of determining the scattered field when the geometrical and physical properties of the scatter are known. The inverse scattering problem is the problem of inferring information on the in-homogeneity from knowledge of the far-field pattern, i.e. the scattered wave at large distances from the scatter. Classical electromagnetic inverse scattering theory provides a rich supply of challenging mathematical problems. First of all, this is due to the fact that the unknown physical conditions where the scattering takes place create difficulties in trying to construct the solution procedure. Second, all the inverse scattering problems significant in applications belong to the class of so-called ill-posed problems in the sense of Hadamard and therefore any reliable approach to their solution must face, at some stage, questions of uniqueness and numerical stability. Using the UWB signal imagery, may obtain the higher solution. Imaging methods (bistatic or monostatic) base on broadband or UWB stimulation signals are usually referred to as migrations.In particular, it is well established that any numerical implementation of a method for the solution of an inverse scattering problem must, at some step, incorporate a regularization procedure in order to eliminate the artificial oscillations due to the ill-posed of the problem.
In this paper, introduce two kinds of method base on IR-UWB: DAS (Delay-And-Sum) and LSM (Linear Sampling Method).Then introduce a modifying method of LSM (MSM). Moreover, we use the Morozov's discrete principle to choice the parameter of regularization.
引文
1 I. I. Immoreeve, D. V. Fedotov. Ultra Wideband Radar Systems: Advantages and Disadvantages.In Proc. IEEE Ultra Wideband Systems and Technologies Conf. May 2002: 201~205.
2 J. Immoreev, James and D. Taylor. The Future of Radars. IEEE on Ultra Wideband Systems and Technology. 2002,2:25~26
3 Muhammad, Dawood. Ultra Wideband Coherent Random Noise Radar Theory and Experiments. University of Nebraska Lincoln Nebraska. 2001:1~9
4 G. Liu, H. Gu. The Development of Random Signal Radar. IEEE Trans AES. 1999, 35(3):770~777
5 S. Hongbo, L. Yilong and L. Guosui. Ultra Wideband Technology and Random Signal Radar on Ideal Combination. IEEE AES System Magazine. 2003,5(2):164~166
6 R. M. Narayanan, Yi Xu and P. D. Hoffimcycr et al. Design Performance and Applications of a Coherent Ultra-wideband Random Noise Radar. Opt. Eng. June 1998,37(6):1855~1869
7 S. Dmitriy, R. M. Gamatyuk and Narayanan. SAR Imaging Using Coherent Ultra Wideband Random Noisc Radar. Proc. SPIE Int. Soc Opt Eng. 1999,3810:223~230
8 K. Lukin, G. Ncsti and A. A. Mogila et al. Short Range Imaging Applications Using Noise Radar Technology. The 3rd European Conference on SAR, Munich Germany, May 2000: 361~365
9 E. K. Walton, K. Lukin and V. Fillimon et al. ISAR Imaging Using UWB Noise Radar. Proceedings of the 18th Annual Meeting & Symposium of the Antenna Measurement Technology Association. Seattle, Sept ~Oct. 1996: 167~171
10张先义,苏卫民,顾红,刘中.噪声超宽带成像雷达技术及其发展.现代雷达. 2006年8月,28(8):7~8
11 T. B. Barret. History of Ultra Wideband Communications and Radar. Part II. Microwave Journal. 2001, Feb:22~53
12刘广平.超宽带合成孔径雷达高效成像算法.国防科学技术大学,2003:35~36
13 D. Tarchi, D. Leva and K. A. Lukin, et al. SAR Imaging Using CW and Pulsed Noise Radar. Proc. of the First International Workshop on the Noise Radar Technology. Sept.2002, Inv.6: 19~20
14 Zhang Yan, R. M. Narayanan and Xu Xiaojian. Theoretical and Simulation Analysis of Random Noise Mono-pulse Radar. Antennas and Propagation Society International Symposium. 2002: 438~389
15 Xu Xiaojian and R. M. Narayanan. Imaging Performance Analysis of a FOPEN UWB Random Noise Radar. Antennas and Propagation Society International Symposium. 2001,4: 273~276
16 Xu Xiaojian, C. B. Daryl and S. G. Dmitriy et al. Coherent Random Radar Imaging. The First International Workshop on the Noise Radar Technology. 2002: 19~20
17 Xu Xiaojian, R. M. Narayanan. FOPEN SAR Imaging UWB Step-frequency and Random Noise Waveforms. IEEE Trans. on AES. Oct.2001, 37(4): 1287~1300
18杨志华,张钦宇,陈萍,许洪光.基于BP神经网络的UWB系统窄脉冲捕获技术研究.通信学报. 2005,(10):8~9
19许洪光,张钦宇,林茂六,王欢,刘晓雷.包络分析在超宽带信号采集中的应用.重庆邮电学院学报(自然科学版). 2006, (03):42~43
20方广有,佐藤原之.频率步进探地雷达及其在地雷探测中的应用.电子学报. 2005,3(3):20~21
21张双狮.伪随机编码脉冲在UWB搜救雷达中的应用.成都理工大学硕士学位论文. 2006:47~48
22 Yuehua Zhao, Wenyi Shao and Gang Wang. UWB Microwave Imaging for Early Breast Cancer Detection: Effect of Two Synthetic Antenna Array Configurations. IEEE International Conference on Systems, Man and Cybernetics. 2004,(5):4468~4473.
23赵或,黄春琳,栗毅,雷文太.超宽带穿墙探测雷达的反向投影成像算法.雷达科学与技术. 2007年2月,5(1):49~59
24林翊青,李景文.超宽带/宽波束SAR的后向投影(BP)算法.遥测遥控. 2005年5月,26(3):24~30
25余洪涛,童宁宁,田建峰.超宽带SAR成像的快速BP算法空军工程大学学报(自然科学版). 2005年10月,6(5):73~75
26朱国富,董臻,梁甸农.超宽带LFM信号的BP成像算法.信号处理. 2001, 17 (5) : 424～428
27 Xu Li, E. J. Bond, B. D. Vanveen and S. C. Hagness. Overview of Ultra Wideband Microwave Imaging via Space-time Beamforming for Early-stage Breast-cancer Detection. IEEE Antennas and Propagation Magazine. Feb.2005,vol.47(No.1):45~50
28 J. Li, P. Stoica and Z. Wang. On Robust Capon Beamforming and Diagonal Loading. IEEE Trans. on Signal Processing. July 2003, vol.51(No.7):77~80
29 Allan, R. Hunt. Image Formation through Walls Using a Distributed Radar Sensor Array. Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop. Aprl.2003,4(1):42~45
30 M. Mahfouz, A. Fathy, Y. Yang, E. E. Ali and A. Badawi. See-through-wall Imaging Using Ultra Wideband Pulse Systems. Proceedings of the 34th Applied Imagery and Pattern Recognition Workshop. 2005, 5(1):65~68
31 N. C. Currie, D. D. Ferris New Low Enforcement Application of Millimeter Wave Radar. Sept.1997, vol.3066: 2~10
32保铮,邢孟道,王彤.雷达成像技术.电子工业出版社. 2005年4月:78~80
33 B. D. Steinberg, H. M. Subbaram. Microwave Imaging Techniques. New York. Wiley Inter Science Publication. 1991:20~21
34 G. Malek, M. Hussain. Principles of Space-Time Array Processing for Ultra Wideband Pulse Radar and Radio Communications. IEEE Transactions on Vehicular Technology. May 2002,Vol.51(3):393~403
35 G. Malek, M. Hussain. Ultra Wideband Impulse Radar an Overview of the Principles. IEEE AES Systems Magazine. September 1998, Vol.42(3):9~14
36 D. Colton, R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer Verlag Berlin Heidelberg New York. 1992:106~126
37 J. B. Keller. Inverse Problem. Am. Math. Mon. 1976, 83: 107~118
38 J. Hadamard. Lectures on the Cauchy Problems in Linear Partial Differential Equations. Yale University Press. New Haven. 1923:124~130
39 D. Colton, R. Kress. Inverse Acoustic and Electromagnetic ScatteringTheory. 2nd edn. Springer Verlag Berlin Heidelberg New York. 1998:30~50
40 A. Kirsch, R. Kress. Uniqueness in Inverse Obstacle Scattering. Inverse Problems. 1993,9: 285–299
41麦宏晏,王连堂.利用线性抽样方法重建Dirichlet边界条件.工程数学报. 2006年8月,23(4):657~659
42 D. Colton, A. Kirsch. A Simple Method for Solving Inverse Scattering Problem in the Resonance Region. Inverse Problem. 1996, 12: 383~393
43 D. L. Phillips. A Technique for the Numerical Solution of Certain Integral Equation of the First Kind. Assoc. Comput. Math. 1962, 9: 84~97
44 A. N. Tikhonov. On Solving Incorrectly Posed Problems and Method of Regularization. Dokl. Acad. Nauk USSR. 1963, 151(3):10~24
45 A. N. Tikhonov, V. Y. Arsenin. Solutions of Ill-posed Problem. Winston and Sons Washington. 1977:17~22
46 A. Kirsch. An Introduction to the Mathematical Theory of Inverse Problem. Springer Verlag Berlin Heidelberg New York. 1996:53~58
47 V. A. Morozov. On the Solution of Functional Equations by the Method of Regularization. Soviet Math. Doklady (English translation). 1966,7: 414~417
48 V. A. Morozov. Choice of parameter for the solution of functional equation by the regularization method. Soviet Math. Doklady (English translation). 1967, 8: 1000~1003
49 V. A. Moroaov. The Error Principle in the Solution of Operational Equations by the Regularization Method. USSR Comput. Math. phys. 1968, 8: 63~87
50 V. A. Morozov. Method for Solving Incorrectly Posed Problems. Springer Verlag Berlin Heidelberg New York. 1984:12~25
51 Ilaria Catapano, Lorenzo Crocco and Tommaso Isernia. On Simple Methods for Shape Reconstruction of Unknown Scatterers. IEEE Transctions on Antennas and Propagation. May 2007,Vol. 55( No. 5): 1434~1435
52 A. Kirsch. Characterization of the Shape of the Scattering Obstacle by the Spectral Data of the Far Field Operator. Inverse Problem. 1998,14: 1489~1512
2 J. Immoreev, James and D. Taylor. The Future of Radars. IEEE on Ultra Wideband Systems and Technology. 2002,2:25~26
3 Muhammad, Dawood. Ultra Wideband Coherent Random Noise Radar Theory and Experiments. University of Nebraska Lincoln Nebraska. 2001:1~9
4 G. Liu, H. Gu. The Development of Random Signal Radar. IEEE Trans AES. 1999, 35(3):770~777
5 S. Hongbo, L. Yilong and L. Guosui. Ultra Wideband Technology and Random Signal Radar on Ideal Combination. IEEE AES System Magazine. 2003,5(2):164~166
6 R. M. Narayanan, Yi Xu and P. D. Hoffimcycr et al. Design Performance and Applications of a Coherent Ultra-wideband Random Noise Radar. Opt. Eng. June 1998,37(6):1855~1869
7 S. Dmitriy, R. M. Gamatyuk and Narayanan. SAR Imaging Using Coherent Ultra Wideband Random Noisc Radar. Proc. SPIE Int. Soc Opt Eng. 1999,3810:223~230
8 K. Lukin, G. Ncsti and A. A. Mogila et al. Short Range Imaging Applications Using Noise Radar Technology. The 3rd European Conference on SAR, Munich Germany, May 2000: 361~365
9 E. K. Walton, K. Lukin and V. Fillimon et al. ISAR Imaging Using UWB Noise Radar. Proceedings of the 18th Annual Meeting & Symposium of the Antenna Measurement Technology Association. Seattle, Sept ~Oct. 1996: 167~171
10张先义,苏卫民,顾红,刘中.噪声超宽带成像雷达技术及其发展.现代雷达. 2006年8月,28(8):7~8
11 T. B. Barret. History of Ultra Wideband Communications and Radar. Part II. Microwave Journal. 2001, Feb:22~53
12刘广平.超宽带合成孔径雷达高效成像算法.国防科学技术大学,2003:35~36
13 D. Tarchi, D. Leva and K. A. Lukin, et al. SAR Imaging Using CW and Pulsed Noise Radar. Proc. of the First International Workshop on the Noise Radar Technology. Sept.2002, Inv.6: 19~20
14 Zhang Yan, R. M. Narayanan and Xu Xiaojian. Theoretical and Simulation Analysis of Random Noise Mono-pulse Radar. Antennas and Propagation Society International Symposium. 2002: 438~389
15 Xu Xiaojian and R. M. Narayanan. Imaging Performance Analysis of a FOPEN UWB Random Noise Radar. Antennas and Propagation Society International Symposium. 2001,4: 273~276
16 Xu Xiaojian, C. B. Daryl and S. G. Dmitriy et al. Coherent Random Radar Imaging. The First International Workshop on the Noise Radar Technology. 2002: 19~20
17 Xu Xiaojian, R. M. Narayanan. FOPEN SAR Imaging UWB Step-frequency and Random Noise Waveforms. IEEE Trans. on AES. Oct.2001, 37(4): 1287~1300
18杨志华,张钦宇,陈萍,许洪光.基于BP神经网络的UWB系统窄脉冲捕获技术研究.通信学报. 2005,(10):8~9
19许洪光,张钦宇,林茂六,王欢,刘晓雷.包络分析在超宽带信号采集中的应用.重庆邮电学院学报(自然科学版). 2006, (03):42~43
20方广有,佐藤原之.频率步进探地雷达及其在地雷探测中的应用.电子学报. 2005,3(3):20~21
21张双狮.伪随机编码脉冲在UWB搜救雷达中的应用.成都理工大学硕士学位论文. 2006:47~48
22 Yuehua Zhao, Wenyi Shao and Gang Wang. UWB Microwave Imaging for Early Breast Cancer Detection: Effect of Two Synthetic Antenna Array Configurations. IEEE International Conference on Systems, Man and Cybernetics. 2004,(5):4468~4473.
23赵或,黄春琳,栗毅,雷文太.超宽带穿墙探测雷达的反向投影成像算法.雷达科学与技术. 2007年2月,5(1):49~59
24林翊青,李景文.超宽带/宽波束SAR的后向投影(BP)算法.遥测遥控. 2005年5月,26(3):24~30
25余洪涛,童宁宁,田建峰.超宽带SAR成像的快速BP算法空军工程大学学报(自然科学版). 2005年10月,6(5):73~75
26朱国富,董臻,梁甸农.超宽带LFM信号的BP成像算法.信号处理. 2001, 17 (5) : 424～428
27 Xu Li, E. J. Bond, B. D. Vanveen and S. C. Hagness. Overview of Ultra Wideband Microwave Imaging via Space-time Beamforming for Early-stage Breast-cancer Detection. IEEE Antennas and Propagation Magazine. Feb.2005,vol.47(No.1):45~50
28 J. Li, P. Stoica and Z. Wang. On Robust Capon Beamforming and Diagonal Loading. IEEE Trans. on Signal Processing. July 2003, vol.51(No.7):77~80
29 Allan, R. Hunt. Image Formation through Walls Using a Distributed Radar Sensor Array. Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop. Aprl.2003,4(1):42~45
30 M. Mahfouz, A. Fathy, Y. Yang, E. E. Ali and A. Badawi. See-through-wall Imaging Using Ultra Wideband Pulse Systems. Proceedings of the 34th Applied Imagery and Pattern Recognition Workshop. 2005, 5(1):65~68
31 N. C. Currie, D. D. Ferris New Low Enforcement Application of Millimeter Wave Radar. Sept.1997, vol.3066: 2~10
32保铮,邢孟道,王彤.雷达成像技术.电子工业出版社. 2005年4月:78~80
33 B. D. Steinberg, H. M. Subbaram. Microwave Imaging Techniques. New York. Wiley Inter Science Publication. 1991:20~21
34 G. Malek, M. Hussain. Principles of Space-Time Array Processing for Ultra Wideband Pulse Radar and Radio Communications. IEEE Transactions on Vehicular Technology. May 2002,Vol.51(3):393~403
35 G. Malek, M. Hussain. Ultra Wideband Impulse Radar an Overview of the Principles. IEEE AES Systems Magazine. September 1998, Vol.42(3):9~14
36 D. Colton, R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer Verlag Berlin Heidelberg New York. 1992:106~126
37 J. B. Keller. Inverse Problem. Am. Math. Mon. 1976, 83: 107~118
38 J. Hadamard. Lectures on the Cauchy Problems in Linear Partial Differential Equations. Yale University Press. New Haven. 1923:124~130
39 D. Colton, R. Kress. Inverse Acoustic and Electromagnetic ScatteringTheory. 2nd edn. Springer Verlag Berlin Heidelberg New York. 1998:30~50
40 A. Kirsch, R. Kress. Uniqueness in Inverse Obstacle Scattering. Inverse Problems. 1993,9: 285–299
41麦宏晏,王连堂.利用线性抽样方法重建Dirichlet边界条件.工程数学报. 2006年8月,23(4):657~659
42 D. Colton, A. Kirsch. A Simple Method for Solving Inverse Scattering Problem in the Resonance Region. Inverse Problem. 1996, 12: 383~393
43 D. L. Phillips. A Technique for the Numerical Solution of Certain Integral Equation of the First Kind. Assoc. Comput. Math. 1962, 9: 84~97
44 A. N. Tikhonov. On Solving Incorrectly Posed Problems and Method of Regularization. Dokl. Acad. Nauk USSR. 1963, 151(3):10~24
45 A. N. Tikhonov, V. Y. Arsenin. Solutions of Ill-posed Problem. Winston and Sons Washington. 1977:17~22
46 A. Kirsch. An Introduction to the Mathematical Theory of Inverse Problem. Springer Verlag Berlin Heidelberg New York. 1996:53~58
47 V. A. Morozov. On the Solution of Functional Equations by the Method of Regularization. Soviet Math. Doklady (English translation). 1966,7: 414~417
48 V. A. Morozov. Choice of parameter for the solution of functional equation by the regularization method. Soviet Math. Doklady (English translation). 1967, 8: 1000~1003
49 V. A. Moroaov. The Error Principle in the Solution of Operational Equations by the Regularization Method. USSR Comput. Math. phys. 1968, 8: 63~87
50 V. A. Morozov. Method for Solving Incorrectly Posed Problems. Springer Verlag Berlin Heidelberg New York. 1984:12~25
51 Ilaria Catapano, Lorenzo Crocco and Tommaso Isernia. On Simple Methods for Shape Reconstruction of Unknown Scatterers. IEEE Transctions on Antennas and Propagation. May 2007,Vol. 55( No. 5): 1434~1435
52 A. Kirsch. Characterization of the Shape of the Scattering Obstacle by the Spectral Data of the Far Field Operator. Inverse Problem. 1998,14: 1489~1512