面向高分辨率遥感光学成像的压缩感知理论及方法研究
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摘要
日益增长的军事需求对星载遥感成像系统的分辨率提出了越来越高的要求。高分辨率成像系统需要更大的探测器像元阵列和更小的像元尺寸，其产生的庞大数据量也给数据存储和实时传输系统带来巨大的压力。压缩感知理论突破香农/奈奎斯特采样定理限制，它充分利用信号稀疏性或可压缩性，以远低于奈奎斯特采样速率采集信号，然后通过求解优化问题，从少量的信号投影值中准确或高精确地重构原始信号。这种新兴信号采集理论为高分辨率成像系统的方法设计提供了一种新的思路。
本文以高分辨率遥感光学成像系统为研究对象，对压缩感知进行基础理论和应用方法研究。
理论研究方面，①分析了完备基下和过完备冗余字典下的图像稀疏表示方法，研究了基于样本图像的K-SVD字典训练和更新方法，为压缩感知理论在成像系统中的应用奠定了基础。②在分析几种常用测量矩阵构造方法和重构性能的基础上，从约束等距性质出发，构造了正交对称循环测量矩阵和分块循环测量矩阵，并利用Golay互补序列对正交对称循环测量矩阵进行了优化设计，仿真实验验证了两类测量矩阵良好的可重构特性。在此基础上，研究了循环测量矩阵构造的硬件实现方法，仿真验证了FPGA构造循环测量矩阵的可行性和高效性。测量矩阵的研究为压缩成像系统信号的获取提供了理论支撑。③研究了两类图像稀疏重构算法，通过对二维图像信号仿真测试，比较了各类算法的性能。针对凸优化算法对二维图像信号重构精度高而重构速度慢的特点，对凸优化算法中的GPSR算法进行了改进，利用分阶段取对数策略，在迭代的不同阶段选取不同的约束参数和迭代终止条件阈值，实现了在迭代前期阶段快速收敛保证运算速度、在迭代后期阶段保证重构精度的效果。重构算法的研究是压缩成像系统图像重构质量的保证。
应用方法方面，①研究了基于频域调制编码和空域孔径编码的高分辨率红外成像方法。其中，频域调制编码成像方法是利用光学透镜的傅里叶变换性质，对变换后的光场进行频域调制，然后利用逆傅里叶变换透镜对调制后的光场逆变换，最后通过下采样操作现实图像的压缩采样；空域孔径编码成像方法是通过对焦平面上的光场进行孔径掩模编码，实现光场的压缩采样。通过数值仿真实验验证了上述两种成像方法的有效性，并进行了对比分析。②研究了基于压缩感知的CMOS压缩成像方法。利用图像的二维行列可分离变换特性，通过CMOS外部电路设计实现图像模拟域内的二维压缩采样。构造了基于DCT变换矩阵的测量矩阵，从累加互相关性方面分析了其可重构特性。设计了压缩采样的硬件电路，利用列像素电流的加权求和实现图像的行变换，利用向量矩阵乘法实现图像的列变换，以实现图像在电流域内的压缩采样。数值仿真实验验证了压缩成像的有效性，这种压缩采样方式降低了数据率，从而缓解了数模转换以及数据存储和传输的压力。
本文研究了面向高分辨率遥感光学成像的压缩感知理论和应用方法，进一步发展和完善了现有压缩感知理论体系，仿真验证了压缩感知在成像系统应用上的有效性，为高分辨率压缩成像系统的设计提供一种新的技术途径。
Spaceborne remote sensing imaging systems call for more stringent requirement ofthe imaging resolution. High resolution imaging systems require larger pixel arrays andsmaller pixel-pitch, the resulting huge amount of data also cause considerable burdenwith regard to data storage and real-time transmission. Compressed sensing (CS) breaksShannon/Nyquist sampling theorem bottleneck. It captures and represents signals at asampling rate significantly below the Nyquist rate, and then original signals can beaccurately or high precisely recovered by solving sparse optimization problems basedon signal sparsity or compressibility. This emerging signal acquisition theory provides anew method for designing high-resolution imaging systems.
In this paper, we mainly research on the basis of the CS theory and its applicationfor high-resolution remote sensing imaging systems.
In theoretical aspect, we have studied three basic theoretical problems.①Theimage sparse representation based on complete basis and over-complete dictionary areanalyzed. The K-SVD dictionary training and update methods based on sample imagesare also researched. These researches pave the way for its application on imagingsystems.②After an analysis of construction methods and recovery performances ofthe common measurement matrices. We put forward a method for constructingorthogonal sysmmetric circulant matrices (OSCM) and block circulant matrices (BCM).The optimization of OSCM is conducted by using Golay complementary. Thesimulations validate the benign reconstruction performance of the two measurementmatrices. On this basis, the hardware implementation of constructing cyclemeasurement matrices is studied, and the FPGA simulations validate the feasibility andefficiency of construction process. These works provide a theoretical support of signalacquirement in compressive imaging system.③Two kinds of image sparsereconstruction algorithms are studied, and their performance are contrastively analyzedthrough simulation experiments on two-dimensional images. Convex optimizationalgorithms are slower but more accurate than pursuit algorithms for two-dimensionalimage reconstruction. Therefore, we studied for improvement of gradient projection forsparse reconstruction (GPSR). The strategy is that the constraint parameter and thetermination threshold are selected differently at various iteration stages. Theseparameter steps are according to logarithmic scale. This strategy ensures that thealgorithm converges fast at the early stages and performs high precision at the laterstages. The research on reconstruction algorithms guarantees imaging quality incompressive imaging systems.
As for application aspect, we have projected two high resolution imaging systems. ①We proposed a high resolution infrared imaging method based on frequency domainmodulation and coded aperture mask. For the frequency domain modulation method, theFourier transform and inverse Fourier transform of images are implemented by opticallenses. The light field after Fourier transform is modulated, and then Compressiveobservations are obtained by downsampling. For coded aperture method in spacedomain, a coded aperture mask is placed on the focal plane in the optical system to codeand capture the light field. The two approaches are validated by numerical experimentsand a comparative analysis is given out.②We researched a CMOS compressiveimaging method based on CS. On the basic property of two-dimensional separabletransform of images, the compressive samples are obtained by designing suitableperipheral circuit for the sensor. The DCT measurement matrix is constructed and itsperformance is analyzed based on cumulative mutual coherence. The circuit designcomprises tow aspects: the row transforms of images are implemented by the currentweighting summation of each column and the column transforms are performed byvector–matrix multiplier (VMM). All these operate in current domain. Experimentalresults demonstrate the effectiveness of the proposed method which reduces the datarate and thus lowers the pressure of digital-to-analog conversion, data storage andtransmission.
In this paper, the theory and application of CS for high-resolution remote sensingoptical imaging have been researched. The work makes a contribution on furtherdevelopment and improvement the CS theory. The proposed application methods havebeen verified by some experiments, which provide a novel approach for designing acompressed imaging system.
本文以高分辨率遥感光学成像系统为研究对象，对压缩感知进行基础理论和应用方法研究。
理论研究方面，①分析了完备基下和过完备冗余字典下的图像稀疏表示方法，研究了基于样本图像的K-SVD字典训练和更新方法，为压缩感知理论在成像系统中的应用奠定了基础。②在分析几种常用测量矩阵构造方法和重构性能的基础上，从约束等距性质出发，构造了正交对称循环测量矩阵和分块循环测量矩阵，并利用Golay互补序列对正交对称循环测量矩阵进行了优化设计，仿真实验验证了两类测量矩阵良好的可重构特性。在此基础上，研究了循环测量矩阵构造的硬件实现方法，仿真验证了FPGA构造循环测量矩阵的可行性和高效性。测量矩阵的研究为压缩成像系统信号的获取提供了理论支撑。③研究了两类图像稀疏重构算法，通过对二维图像信号仿真测试，比较了各类算法的性能。针对凸优化算法对二维图像信号重构精度高而重构速度慢的特点，对凸优化算法中的GPSR算法进行了改进，利用分阶段取对数策略，在迭代的不同阶段选取不同的约束参数和迭代终止条件阈值，实现了在迭代前期阶段快速收敛保证运算速度、在迭代后期阶段保证重构精度的效果。重构算法的研究是压缩成像系统图像重构质量的保证。
应用方法方面，①研究了基于频域调制编码和空域孔径编码的高分辨率红外成像方法。其中，频域调制编码成像方法是利用光学透镜的傅里叶变换性质，对变换后的光场进行频域调制，然后利用逆傅里叶变换透镜对调制后的光场逆变换，最后通过下采样操作现实图像的压缩采样；空域孔径编码成像方法是通过对焦平面上的光场进行孔径掩模编码，实现光场的压缩采样。通过数值仿真实验验证了上述两种成像方法的有效性，并进行了对比分析。②研究了基于压缩感知的CMOS压缩成像方法。利用图像的二维行列可分离变换特性，通过CMOS外部电路设计实现图像模拟域内的二维压缩采样。构造了基于DCT变换矩阵的测量矩阵，从累加互相关性方面分析了其可重构特性。设计了压缩采样的硬件电路，利用列像素电流的加权求和实现图像的行变换，利用向量矩阵乘法实现图像的列变换，以实现图像在电流域内的压缩采样。数值仿真实验验证了压缩成像的有效性，这种压缩采样方式降低了数据率，从而缓解了数模转换以及数据存储和传输的压力。
本文研究了面向高分辨率遥感光学成像的压缩感知理论和应用方法，进一步发展和完善了现有压缩感知理论体系，仿真验证了压缩感知在成像系统应用上的有效性，为高分辨率压缩成像系统的设计提供一种新的技术途径。
Spaceborne remote sensing imaging systems call for more stringent requirement ofthe imaging resolution. High resolution imaging systems require larger pixel arrays andsmaller pixel-pitch, the resulting huge amount of data also cause considerable burdenwith regard to data storage and real-time transmission. Compressed sensing (CS) breaksShannon/Nyquist sampling theorem bottleneck. It captures and represents signals at asampling rate significantly below the Nyquist rate, and then original signals can beaccurately or high precisely recovered by solving sparse optimization problems basedon signal sparsity or compressibility. This emerging signal acquisition theory provides anew method for designing high-resolution imaging systems.
In this paper, we mainly research on the basis of the CS theory and its applicationfor high-resolution remote sensing imaging systems.
In theoretical aspect, we have studied three basic theoretical problems.①Theimage sparse representation based on complete basis and over-complete dictionary areanalyzed. The K-SVD dictionary training and update methods based on sample imagesare also researched. These researches pave the way for its application on imagingsystems.②After an analysis of construction methods and recovery performances ofthe common measurement matrices. We put forward a method for constructingorthogonal sysmmetric circulant matrices (OSCM) and block circulant matrices (BCM).The optimization of OSCM is conducted by using Golay complementary. Thesimulations validate the benign reconstruction performance of the two measurementmatrices. On this basis, the hardware implementation of constructing cyclemeasurement matrices is studied, and the FPGA simulations validate the feasibility andefficiency of construction process. These works provide a theoretical support of signalacquirement in compressive imaging system.③Two kinds of image sparsereconstruction algorithms are studied, and their performance are contrastively analyzedthrough simulation experiments on two-dimensional images. Convex optimizationalgorithms are slower but more accurate than pursuit algorithms for two-dimensionalimage reconstruction. Therefore, we studied for improvement of gradient projection forsparse reconstruction (GPSR). The strategy is that the constraint parameter and thetermination threshold are selected differently at various iteration stages. Theseparameter steps are according to logarithmic scale. This strategy ensures that thealgorithm converges fast at the early stages and performs high precision at the laterstages. The research on reconstruction algorithms guarantees imaging quality incompressive imaging systems.
As for application aspect, we have projected two high resolution imaging systems. ①We proposed a high resolution infrared imaging method based on frequency domainmodulation and coded aperture mask. For the frequency domain modulation method, theFourier transform and inverse Fourier transform of images are implemented by opticallenses. The light field after Fourier transform is modulated, and then Compressiveobservations are obtained by downsampling. For coded aperture method in spacedomain, a coded aperture mask is placed on the focal plane in the optical system to codeand capture the light field. The two approaches are validated by numerical experimentsand a comparative analysis is given out.②We researched a CMOS compressiveimaging method based on CS. On the basic property of two-dimensional separabletransform of images, the compressive samples are obtained by designing suitableperipheral circuit for the sensor. The DCT measurement matrix is constructed and itsperformance is analyzed based on cumulative mutual coherence. The circuit designcomprises tow aspects: the row transforms of images are implemented by the currentweighting summation of each column and the column transforms are performed byvector–matrix multiplier (VMM). All these operate in current domain. Experimentalresults demonstrate the effectiveness of the proposed method which reduces the datarate and thus lowers the pressure of digital-to-analog conversion, data storage andtransmission.
In this paper, the theory and application of CS for high-resolution remote sensingoptical imaging have been researched. The work makes a contribution on furtherdevelopment and improvement the CS theory. The proposed application methods havebeen verified by some experiments, which provide a novel approach for designing acompressed imaging system.
引文
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