直接解调方法的研究与应用
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摘要
在高能天文低信噪比、低统计性和低分辨率的数据处理中,直接解调方法已经发展成为一套具有很强成像和解谱能力的直接方法。这一方法的精髓是在迭代求解调制方程的过程中加入物理条件约束。该方法充分利用了调制方程所包含的对象信息、突破了传统成像技术所受仪器内禀角分辨能力的限制,从而实现高分辨率、高精度成像。但该方法要耗费大量的内存和计算时间,收敛较慢,这就限制了它的运用。本文对直接解调方法进行了深入的研究:首先采用稀疏矩阵存储响应矩阵并进行有关计算以节省内存和计算量,采用Ordered-Subsets方法加快迭代的收敛速度;然后提出了适用于平移不变系统的卷积形式,通过快速Fourier变换来进行快速计算,使直接解调方法得到了更大的加速并彻底解决这类系统的响应矩阵的存储问题。这些方法在一定条件下可以相互结合使用,从而能够达到更高的性能。在此基础上,本文将直接解调方法运用于编码板系统和准直调制型望远镜HE/HXMT的数据处理,提出了在图像重建过程中加入权重因子的方法,解决了探测的不均匀性带来的权重问题;提出SDDM解决了利用平移不变系统的低采样率的数据进行高分辨率的成像时平移不变性被破坏的问题;提出了MDDM解决了直接解调方法的卷积形式在HE/HXMT这种多探测器的准直调制型望远镜中不能直接运用的问题等等。而这些问题在其它的观测设备中也经常出现。这些问题得到解决之后,本文运用SDDM将编码板系统的角分辨率提高了约一个数量级,用模拟计算的方法计算并给出了HE/HXMT巡天成像的主要性能指标,还给出了HE/HXMT的几种不同的准直器视场方案的定点观测及扫描成像能力,给HE/HXMT的优化设计提供了参考数据,发现将现有的18种视场的设计改为2种视场并不会影响成像性能,但后者可以大大减少数据处理的复杂度,更可以结合本文提出的偏轴观测的定点观测方式大幅提高定点观测的精度。另外,本文还提出了基于直接解调方法的快视成像,它可以利用HXMT的一维扫描数据获得二维的图像,从而可以利用HXMT的巡天数据实现近实时成像。最后,本文在面向对象的程序设计思想的指导下设计并开发了直接解调方法程序库,利用该库人们不用了解直接解调方法及其各种加速算法的细节就能快捷方便的编写出高性能的直接解调成像程序。
In the analyses of low signal-noise-ratio, low statistical and low resolution data in high energy astrophysics, the Direct Demodulation Method (DDM) has been developed into a powerful method for image and spectrum recoveries. The main idea of DDM is resolving the modulation equation iteratively with physical constraints. DDM can use the information contained in the modulation equation sufficiently and derive images of higher resolution than the intrinsic resolution of instruments, which limits the resolution of conventional image reconstruction methods. However, DDM costs much memories and computation time and converges slowly. This restricts its applications. This thesis makes an in-depth study on DDM, optimizes it by three methods: Sparse matrices are used for the store of response matrices and corresponding computation to reduce the requirements for memories and computation time; Ordered-Subsets method is used to make iterations converge faster; The formula of iterations is transformed into convolution form for shift-invariant systems. The convolution form of DDM makes the storage of response matrix not a problem anymore and the convolutions can be computed by fast Fourier transform rapidly. These methods can be combined under certain conditions to achieve better performance. Based on these methods,DDM is applied to the data process of the coded mask system of IBIS/INTEGRAL and a collimated modulation telescope HE/HXMT. Some problems are solved, which arise when DDM and conventional cross-correlation method are used to deal with the real data from these two instruments. These problems include the problem brought by the unevenness of observations, the problem that the shift-invariant property is broken when low-sampling-rate data of shift-invariant system are used to derive high resolution images, the problem that the convolution form of DDM cannot be directly used to deal with the data of multidetector- collimated-modulation telescope like HE/HXMT, etc. These problems also often arise in data processing of other instruments. Based on the solutions to these problems, the angular resolution of coded mask systems is improved by about an order of magnitude, and the main performances of the all-sky survey of HE/HXMT, such as sensitivity, resolution, locating accuracy, etc, is obtained by simulation study. The simulation study also compares the performances of pointed observations and scanning imaging of different schemes of collimators. This comparison provides insights for the optimization of HE/HXMT, indicating that reducing the number of the types of FOVs from 18 to 2 would not degrade the imaging performance, but would decrease the complication of the data processing and increase the accuracy of off-axis pointed observations. Quick-look imaging, which is based on DDM, is proposed to obtain near-real-time two-dimensional images from one-dimensional scanning data. Finally, DDM library is designed and developed under the object-oriented programming methodology. Users of DDM library can write high-performance programs without much knowledge of DDM and the methods to accelerate it.
In the analyses of low signal-noise-ratio, low statistical and low resolution data in high energy astrophysics, the Direct Demodulation Method (DDM) has been developed into a powerful method for image and spectrum recoveries. The main idea of DDM is resolving the modulation equation iteratively with physical constraints. DDM can use the information contained in the modulation equation sufficiently and derive images of higher resolution than the intrinsic resolution of instruments, which limits the resolution of conventional image reconstruction methods. However, DDM costs much memories and computation time and converges slowly. This restricts its applications. This thesis makes an in-depth study on DDM, optimizes it by three methods: Sparse matrices are used for the store of response matrices and corresponding computation to reduce the requirements for memories and computation time; Ordered-Subsets method is used to make iterations converge faster; The formula of iterations is transformed into convolution form for shift-invariant systems. The convolution form of DDM makes the storage of response matrix not a problem anymore and the convolutions can be computed by fast Fourier transform rapidly. These methods can be combined under certain conditions to achieve better performance. Based on these methods,DDM is applied to the data process of the coded mask system of IBIS/INTEGRAL and a collimated modulation telescope HE/HXMT. Some problems are solved, which arise when DDM and conventional cross-correlation method are used to deal with the real data from these two instruments. These problems include the problem brought by the unevenness of observations, the problem that the shift-invariant property is broken when low-sampling-rate data of shift-invariant system are used to derive high resolution images, the problem that the convolution form of DDM cannot be directly used to deal with the data of multidetector- collimated-modulation telescope like HE/HXMT, etc. These problems also often arise in data processing of other instruments. Based on the solutions to these problems, the angular resolution of coded mask systems is improved by about an order of magnitude, and the main performances of the all-sky survey of HE/HXMT, such as sensitivity, resolution, locating accuracy, etc, is obtained by simulation study. The simulation study also compares the performances of pointed observations and scanning imaging of different schemes of collimators. This comparison provides insights for the optimization of HE/HXMT, indicating that reducing the number of the types of FOVs from 18 to 2 would not degrade the imaging performance, but would decrease the complication of the data processing and increase the accuracy of off-axis pointed observations. Quick-look imaging, which is based on DDM, is proposed to obtain near-real-time two-dimensional images from one-dimensional scanning data. Finally, DDM library is designed and developed under the object-oriented programming methodology. Users of DDM library can write high-performance programs without much knowledge of DDM and the methods to accelerate it.
引文
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[2] Li Tipei, Wu Mei. Reconstruction of objects by direct demodulation. Ap&SS, 1994, 215, 213
[3]李惕碚,吴枚.高能天文中成像和解谱的直接方法.天体物理学报, 1993, 13, 215
[4] Li Tipei, Wu Mei. Direct Method of Image and Spectrum Recovery in High-Energy Astronomy. ChA&A, 1993, 17, 453
[5] Li Tipei, Wu Mei, Lu Zhuguo, et al. Modulation imaging based on a direct deconvolution technique. Ap&SS, 1993, 205, 381
[6] Gull S F, Daniell G J. Image reconstruction from incomplete and noisy data. Nature, 272, 686
[7] Pollock A M T, Bignami G F, Hermsen W, et al. Search for gamma-radiation from extragalactic objects using a likelihood method. A&A, 1981, 94, 116
[8] H?gbom J. Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines, A&AS, 15, 417
[9] Schwarz U J. Mathematical-statistical Description of the Iterative Beam Removing Technique (Method CLEAN), A&A, 1978, 65, 345
[10] Richardson W H. Bayesian-based iterative method of image restoration. J. Opt. Soc. Am., 62, 55
[11] Lucy L B. An iterative technique for the rectification of observed distributions. AJ, 79, 745
[12] Li Tipei. Space observation of hard X-rays, in: Hu W R (ed.) Space Science in China, Gordon & Breach Science Publisher
[13] Feng Hua, Chen Yong, Zhang Shuangnan, et al. Improving the spatial resolution of XMM-Newton EPIC images by direct demodulation technique. A&A, 2003, 402, 1151
[14] Warwick R S, Norton A J, Turner M J L, et al. A survey of the galactic plane with EXOSAT. MNRAS, 1988, 232, 551
[15] Lu Fangjun, Li Tipei, Sun Xuejun, et al. X-ray map from the EXOSAT galactic plane survey and a direct demodulation technique. A&AS, 1996, 115, 395
[16] Thompson R J, Shelton R G, Arning C A. Initial Results of a Comprehensive Ultrasoft Survey of the Einstein IPC Database: Source List and Confirmation of the Selection Procedure. AJ, 115, 2587
[17] Matteson J L, The UCSD/MIT hard X-ray and low energy gamma-ray experiment for HEAO-1 - Design and early results, Proc. AIAA, No. 78-35
[18] Levine A M, Lang F L, Lewin W H G, et al. The HEAO1 A-4 catalog of high-energy X-ray sources, ApJS, 54, 581
[19] Lu Fangjun, Li Tipei, Sun Xuejun, et al. In Shellard & Nguyen (eds) Proceedings of CHEP’95, 848
[20]宋黎明,李惕碚,崔伟.用ASM/RXTE数据对Crab天区的直接解调成像.天体物理学报. 1999, NO. 1: 27
[21] Chen Yong, Li Tipei, Wu Mei. Direct demodulation technique for rotating modulation collimator imaging. A&AS, 1998, 128, 363
[22] Lu Fangjun, Aschenbach B, Song Liming. Observations of the supernova remnant G54.1+0.3: X-ray spectrum and evidence for an X-ray jet. A&A, 2001, 370, 570
[23] Zhang Shu, Li Tipei, Wu Mei. COMPTEL observation of the flaring quasar PKS0528+134. A&A, 1998, 340, 62
[24]张澍,李惕碚,吴枚. Comptonγ射线望远镜的直接解调成像.天体物理学报,1997,17,263-270
[25]黎刚.直接解调法在STM图像和SR实验重建中的应用.中科院高能所,硕士论文2001
[26]孙飞,薛平,袁韬.光学相干层析成像的图象重建.光学学报, 2000, 20, 1043
[27] Li Tipei, Zhang Shuangnan, Lu Fangjun. Hard X-ray Modulation Telescope (HXMT) Mission. Chinese Journal of Space Science, 2006, 26(Supplement), 30
[28] Lu Zhuguo, Wang Jianzhong, Li Yanguo, et al. Hard X-ray imaging with a slat collimated telescope. Nuclear Instruments and Methods in Physics Research Section A, 362, 551
[29]“十一五”空间科学发展规划项目建议书:硬X射线调制望远镜(HXMT). [2005]
[30] Shepp L A, Vardi Y. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imag., 1982, 2, 113
[31] Malcolm H H, Richard S L. Accelerated Image Reconstruction Using Ordered Subsets of Projection Data. IEEE Trans. Med. Imag., 1994, 13, 601
[32] Cooley J W, Tukey J W. An algorithm for the machine computation of complex Fourier series. Mathematics of Compuation. 1965, 19, 297
[33] FFTW Home Page: http://www.fftw.org
[34] User’s Manual for FFTW. [2006-06-23]. http://www.fftw.org/fftw3.pdf
[35] Intel Math Kernel Library 9.1 Overview. [2007-03]. http://www.intel.com/cd/software/ products/asmo-na/eng/307757.htm
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[37] Buck I, Foley T, Horn D, et al. Brook for GPUs: Stream Computing on Graphics Hardware. ACM Transactions on Graphics, 2004, Special Issue, 23(3), 777
[38] NVIDIA CUDA Homepage. [2007-10-11]. http://developer.nvidia.com/object/cuda.html
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[40] Caroli E, Stephen J B, Di Cocco G, et al. Coded aperture imaging in X- and gamma-ray astronomy. Space Sci. Rev., 1987, 45, 349
[41] Goldwurm A. Imaging Techniques Applied to the Coded Mask SIGMA Telescope. Exper. Astron., 6, 9
[42] Skinner G K. Coding (and Decoding) Coded Mask Telescopes. Exper. Astron., 1995, 6, 1
[43] Fenimore E E, Cannon T M. Coded aperture imaging with uniformly redundant arrays. Appl. Opt., 1978, 17, 337
[44] Paul J, Ballet J, Cantin M, et al. Sigma - The hard X-ray and soft gamma-ray telescope on board the GRANAT space observatory. AdSpR, 1991, 11, 289
[46] Gros A, Goldwurm A, Cadolle-Bel M, et al. The INTEGRAL IBIS/ISGRI System Point Spread Function and Source Location Accuracy. A&A, 2003, 411, 179
[47] Winkler C, Courvoisier T J-L, Di Cocco G, et al. The INTEGRAL_Mission. A&A, 2003, 411, 1
[48] Ubertini P, Lebrun F, Di Cocco G, et al. IBIS: The Imager on-board INTEGRAL. A&A, 2003, 411, 131
[49] Lebrun F, Leray J-P, Lavocat P, et al. ISGRI: the INTEGRAL Soft Gamma-Ray Imager. A&A, 2003, 411, 141
[50] Di Cocco G, Caroli E, Celesti E, et al. IBIS/PICsIT in-flight performances. A&A, 2003, 411, 189
[51] Introduction to the INTEGRAL Data Analysis. [2005-11-24]. http://isdc.unige.ch/Soft/ download/osa/osa_doc/osa_doc-7.0/osa_um_intro-5.1.pdf
[52] IBIS Analysis User Manual. [2007-09-15]. http://isdc.unige.ch/Soft/download/osa/osa_doc/ osa_doc-7.0/osa_um_ibis-7.0.pdf
[53] Gehrels N. The Swiftγ-ray burst mission. New Astronomy Reviews, 2004, 48, 431
[54] Barthelmy S D, Barbier L M, Cummings J R, et al. The Burst Alert Telescope (BAT) on the SWIFT Midex Mission. Space Science Reviews, 2005, 120, 143
[55] Markwardt C B, Tueller J, Skinner G K, et al. THE SWIFT/BAT HIGH-LATITUDE SURVEY: FIRST RESULTS. ApJ, 2005, 633, 77
[56]硬X射线调制望远镜(HXMT)地面应用系统方案可行性论证报告. [2007].中国科学院高能物理研究所粒子天体物理实验室
[57] HUSDC软件需求分析说明书. [2006].清华大学天体物理中心
[58] HUSDC总体技术方案. [2007].清华大学天体物理中心
[59] Jacobson I, Christenson M, Jonsson P, et al. OBJECT-ORIENTED SOFTWARE ENGINEERING: A Use Case Driven Approach. New York: Addison-Wesley Publishing Co., 1992
[60] Stroustrup B. The C++ Programming Language. Special Third Edition. New York: Addison-Wesley Publishing Co., 2000
[61] International Standard: ISO/IEC 14882 Programming languages—C++. Second Edition, 2003-10-15
[62]谭浩强. C程序设计.北京:清华大学出版社, 1991
[63] Lawson C L, Hanson R J, Kincaid D, et al. Basic Linear Algebra Subprograms for FORTRAN usage. ACM Trans. Math. Soft., 1979, 5, 308
[64] Dongarra J J, Du Croz J, Hammarling S, et al. An extended set of FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 1988, 14, 1
[65] Dongarra J J, Du Croz J, Hammarling S, et al. Algorithm 656: An extended set of FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 1988, 14, 18
[66] Dongarra J J, Du Croz J, Duff I S, et al., A set of Level 3 Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 1990, 16, 1
[67] Dongarra J J, Du Croz J, Duff I S, et al., Algorithm 679: A set of Level 3 Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 1990, 16, 18
[68] Blackford L S, Demmel J, Dongarra J, et al. An Updated Set of Basic Linear Algebra Subprograms (BLAS). ACM Trans. Math. Soft., 2002, 28-2, 135
[69] C interface to the legacy BLAS. [2007]. http://www.netlib.org/blas/blast-forum/ cinterface.pdf