基于相位差异的地基望远镜图像恢复算法与GPU高速实现
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摘要
地基望远镜的成像分辨率会受到大气湍流和成像系统误差的影响，特别是大气湍流引起的波前相位畸变会随着望远镜的口径增大而愈加严重，使得目标成像模糊、光能分散、成像质量明显下降，从而限制了地基望远镜的探测能力。相位差异(Phase Diversity, PD)作为一种能够克服光学图像波前畸变的技术已经在地基望远镜图像恢复中得到了广泛的应用。它的基本过程是同时采集具有已知相位差异信息的一对短曝光图像，通过极大似然估计理论构建迭代优化模型，联合估计目标图像和波前相位信息，进而恢复出理想图像。PD技术光路简单、系统构建简易，适应的目标范围广，是一种高性价比的克服大气湍流、获取清晰图像的技术。
本文在分析国内外研究进展的基础上，进行了大量的仿真及实验工作，对PD图像恢复技术的原理、性能改进和实际应用进行了深入的探讨和分析，并对其在GPU并行处理平台上的快速实现进行了大量的验证，具体开展的工作如下：
1、通过理论分析和仿真，分析了PD存在的误差因素，改进和完善了PD数学模型：针对图像噪声影响算法收敛性的问题，建立了一种基于Butterworth低通滤波器的自适应滤波器，提高图像恢复质量的同时，减少算法的迭代次数，缩减了整体迭代的时间；针对多通道图像之间的配准问题，探讨了一种两步图像自动配准算法，利用相位相关结合最小二乘曲面拟合的方法，实现了亚像素级的图像配准，提高了配准的可靠性和精度。
2、PD算法恢复图像时运算量较大，基于CPU的PD软件难以快速恢复图像，使用DSP和FPGA进行硬件加速，是最直接的想法。但是PD目标函数结构复杂，硬件实现也比较复杂。因此，本文利用Zernike多项式的性质，提出了一种PD目标函数的改造方法，在每次计算目标函数时只进行多项式运算，不但易于硬件实现而且也能充分利用硬件并行运算的优势。
3、提出了一种CPU+GPU异构模式的PD算法框架，结合CUDA编程的特点，分析了PD算法的特点，对其进行了像素级的并行化处理，本文将PD中最耗时的目标函数及其导数的构建过程放入GPU中进行并行计算，迭代控制仍由CPU完成，从而充分利用了GPU的并行计算能力，发挥其高性能计算的优势，协同CPU完成PD运算。
4、对PD技术进行了一系列外场实验研究，在PD高速计算系统中完成了对近地扩展目标和天体目标的恢复。实验结果表明，基于PD的图像恢复技术在一定程度上能够克服大气扰动对地基望远镜高分辨率成像的影响，实现点目标和扩展目标的高分辨率成像，具体体现在：使原本不可见的恒星得以清晰显现，其半高全宽值下降了约50%；将0.4″的双星从无法分辨的散斑噪声中恢复出来，双星分辨明显；使原本模糊的、无法辨识的扩展目标轮廓清晰、细节明显。同时，该系统有效地提高了PD图像恢复速度，相比CPU平台获得了近百倍的加速比，改进了系统的实时性，从而使得PD技术能够很好地应用到实际望远镜成像系统中。
The imaging resolution of ground-based telescope is seriously limited by theeffects of atmosphere turbulence and optical system aberrations. Especially is theatmosphere turbulence induced distortion more serious with larger aperture thatmakes the performance of imaging degraded, with the results that the detectionability of large ground-based telescope is restricted. Phase Diversity (PD) techniquethat can overcome wavefront distortions becomes an important developmentaldirection of image restoration for ground-based telescope. By making use ofmaximum likelihood estimate to construct iterative optimization model, it jointlyestimates image of object and wavefront phase from simultaneous collection ofpairs of short exposure image with known phase diversity. It is a highperformance-price ratio method of simple configuration, low cost and well fit forboth point sources and extended sources.
In this paper, referred to research advances in domestic and overseas, a largenumber of numerical simulations and experiments are carried out, consequently，PD algorithm is discussed and analyzed in depth. Besides, the performance of itshigh speed implementation on GPU parallel processing platform is verified. Themain works and achievements are as follows:
1. After analysis for the error factors found in PD test bed alignment and data processing procedure, mathematical model of PD is improved. An adaptive filterbased on Butterworth low pass filter is suggested to reduce noise effect, filter therestored image and at the same time improve convergence properties, so as to reducethe overall computational time. Meanwhile, a two-step auto registration method toimprove the reliability and accuracy, by use of phase correlation combined with leastsquare surface fitting, is proposed.
2. It is difficult to achieve real time application of PD on CPU, and DSP andFPGA is a proper way to improve its performance. While the complex structure ofthe PD objective function influences on its hardware implementation. According tothe theory of Zernike polynomial, a method to modify the PD objective function isproposed, by which the computation of the PD objective function only depends onthe polynomial and the hardware implementation of DSP, FPGA and parallelism ofhardware processing are more easily.
3. PD algorithm is suitable for parallel computing based on GPU, by reasons ofits data partitioning features. Thus a parallel algorithm of PD based on theheterogeneous architecture consisted of CPU and GPU is proposed. According to theanalysis for PD algorithm based on CPU, using the programmer friendly CUDAframe, the parallelization on pixel level is achieved. The construction of objectivefunction and its derivative, the most time consuming part, is transplanted to the GPUplatform, while the iterative process is still controlled by CPU. Accordingly, thespeed of PD image restoration can be greatly increased by taking full advantages ofGPU parallel computing power and floating point calculations.
4. A series of PD experiments are implemented on the high speed computingsystem, including restoration of spread target near ground and spatial objects. Theexperimental results show that PD image restoration technique can significantlyimprove the imaging quality of ground-based telescope imaging system. It makes asingle invisible star to be detected and full width half maximum decrease by50%,the undistinguishable binary star with a separation of0.4″is successfully resolvedfrom speckle noise, and details of spread target which are too fuzzy to be identified are improved to the level of identifiable. Meanwhile，under the premise of the qualityof image can be guaranteed, the CUDA implementation can obtain speedup of up totwo orders of magnitude over the CPU serial implementation. The real time abilityof PD image restoration procedure is effectively improved that makes the PDtechnique more practical in the telescope imaging system.
本文在分析国内外研究进展的基础上，进行了大量的仿真及实验工作，对PD图像恢复技术的原理、性能改进和实际应用进行了深入的探讨和分析，并对其在GPU并行处理平台上的快速实现进行了大量的验证，具体开展的工作如下：
1、通过理论分析和仿真，分析了PD存在的误差因素，改进和完善了PD数学模型：针对图像噪声影响算法收敛性的问题，建立了一种基于Butterworth低通滤波器的自适应滤波器，提高图像恢复质量的同时，减少算法的迭代次数，缩减了整体迭代的时间；针对多通道图像之间的配准问题，探讨了一种两步图像自动配准算法，利用相位相关结合最小二乘曲面拟合的方法，实现了亚像素级的图像配准，提高了配准的可靠性和精度。
2、PD算法恢复图像时运算量较大，基于CPU的PD软件难以快速恢复图像，使用DSP和FPGA进行硬件加速，是最直接的想法。但是PD目标函数结构复杂，硬件实现也比较复杂。因此，本文利用Zernike多项式的性质，提出了一种PD目标函数的改造方法，在每次计算目标函数时只进行多项式运算，不但易于硬件实现而且也能充分利用硬件并行运算的优势。
3、提出了一种CPU+GPU异构模式的PD算法框架，结合CUDA编程的特点，分析了PD算法的特点，对其进行了像素级的并行化处理，本文将PD中最耗时的目标函数及其导数的构建过程放入GPU中进行并行计算，迭代控制仍由CPU完成，从而充分利用了GPU的并行计算能力，发挥其高性能计算的优势，协同CPU完成PD运算。
4、对PD技术进行了一系列外场实验研究，在PD高速计算系统中完成了对近地扩展目标和天体目标的恢复。实验结果表明，基于PD的图像恢复技术在一定程度上能够克服大气扰动对地基望远镜高分辨率成像的影响，实现点目标和扩展目标的高分辨率成像，具体体现在：使原本不可见的恒星得以清晰显现，其半高全宽值下降了约50%；将0.4″的双星从无法分辨的散斑噪声中恢复出来，双星分辨明显；使原本模糊的、无法辨识的扩展目标轮廓清晰、细节明显。同时，该系统有效地提高了PD图像恢复速度，相比CPU平台获得了近百倍的加速比，改进了系统的实时性，从而使得PD技术能够很好地应用到实际望远镜成像系统中。
The imaging resolution of ground-based telescope is seriously limited by theeffects of atmosphere turbulence and optical system aberrations. Especially is theatmosphere turbulence induced distortion more serious with larger aperture thatmakes the performance of imaging degraded, with the results that the detectionability of large ground-based telescope is restricted. Phase Diversity (PD) techniquethat can overcome wavefront distortions becomes an important developmentaldirection of image restoration for ground-based telescope. By making use ofmaximum likelihood estimate to construct iterative optimization model, it jointlyestimates image of object and wavefront phase from simultaneous collection ofpairs of short exposure image with known phase diversity. It is a highperformance-price ratio method of simple configuration, low cost and well fit forboth point sources and extended sources.
In this paper, referred to research advances in domestic and overseas, a largenumber of numerical simulations and experiments are carried out, consequently，PD algorithm is discussed and analyzed in depth. Besides, the performance of itshigh speed implementation on GPU parallel processing platform is verified. Themain works and achievements are as follows:
1. After analysis for the error factors found in PD test bed alignment and data processing procedure, mathematical model of PD is improved. An adaptive filterbased on Butterworth low pass filter is suggested to reduce noise effect, filter therestored image and at the same time improve convergence properties, so as to reducethe overall computational time. Meanwhile, a two-step auto registration method toimprove the reliability and accuracy, by use of phase correlation combined with leastsquare surface fitting, is proposed.
2. It is difficult to achieve real time application of PD on CPU, and DSP andFPGA is a proper way to improve its performance. While the complex structure ofthe PD objective function influences on its hardware implementation. According tothe theory of Zernike polynomial, a method to modify the PD objective function isproposed, by which the computation of the PD objective function only depends onthe polynomial and the hardware implementation of DSP, FPGA and parallelism ofhardware processing are more easily.
3. PD algorithm is suitable for parallel computing based on GPU, by reasons ofits data partitioning features. Thus a parallel algorithm of PD based on theheterogeneous architecture consisted of CPU and GPU is proposed. According to theanalysis for PD algorithm based on CPU, using the programmer friendly CUDAframe, the parallelization on pixel level is achieved. The construction of objectivefunction and its derivative, the most time consuming part, is transplanted to the GPUplatform, while the iterative process is still controlled by CPU. Accordingly, thespeed of PD image restoration can be greatly increased by taking full advantages ofGPU parallel computing power and floating point calculations.
4. A series of PD experiments are implemented on the high speed computingsystem, including restoration of spread target near ground and spatial objects. Theexperimental results show that PD image restoration technique can significantlyimprove the imaging quality of ground-based telescope imaging system. It makes asingle invisible star to be detected and full width half maximum decrease by50%,the undistinguishable binary star with a separation of0.4″is successfully resolvedfrom speckle noise, and details of spread target which are too fuzzy to be identified are improved to the level of identifiable. Meanwhile，under the premise of the qualityof image can be guaranteed, the CUDA implementation can obtain speedup of up totwo orders of magnitude over the CPU serial implementation. The real time abilityof PD image restoration procedure is effectively improved that makes the PDtechnique more practical in the telescope imaging system.
引文
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