压缩感知关键技术研究
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摘要
压缩感知（CS）理论指出，对于稀疏或可压缩信号，采样速率不决定于信号的带宽，而决定于信息在信号中的结构和内容。目前压缩感知的理论和应用研究已经取得了一些成果，但是仍然有大量开放问题尚待研究。针对目前存在的问题，本文研究了方向变换，特征字典，视频分析，压缩成像等关键技术，选题具有重要的理论意义和较高的实用价值。本文主要创新点如下：
(1)研究了在图像的CS重构中使用方向变换。采用分块随机图像采样与基于投影的重构相结合的一般框架，不仅提高了稀疏性，也提高了光滑性。这个框架便于在CS重构过程中加入基于方向变换的Contourlets和双树复小波。得到的算法具有基于投影的CS重构的快速运算速度，而平滑步骤与增强的方向性相结合，有助于获得更好的图像质量，尤其是在低采样率时。
(2)利用Hough变换域的稀疏性，建立起形状的稀疏表示字典，用CS方法寻找图像中的参数化形状。进行了用CS方法从含有噪声的图像的少量测量中检测直线和圆等图形的实验。实验表明CS方法能够得到比Hough变换更干净的检测结果。分析了检测率与信噪比，检测率与测量数的关系。
(3)提出一个适合隐私保护的视频监控应用的编码方案，能够跟踪视频目标而不需要重构视频序列。该方案利用每帧有限数量的伪随机投影编码一个视频序列，解码器利用背景消除图像所具有的稀疏性并重构前景目标的位置。该方案采用粒子滤波器预测目标位置，再用估计的位置作为先验知识改进前景目标位置的重构。隐私保护体现在只采用编码的随机投影不可能重构原始视频内容，安全性体现在如果没有用来产生随机投影的种子，就无法解码。
(4)压缩感知共焦显微镜（CCM）用数字微镜阵列（DMD）高效扫描2D或3D标本，其测量的数据来自针孔照亮的标本像素的随机集合，线性组合（投影）之后用单个光电检测器和测量。与传统CM或PAM相比，CCM能够简化共焦成像的硬件和光学系统的复杂性，将处理从数据采集步骤转移到软件图像重构，降低了成像系统的成本。CCM还以降低的采样速率提供了共焦成像的独特光学切片性质。3D联合重构方法充分利用3D图像图层之间的相关性，进一步提高了系统性能。与2D逐层方法相比，这种3D方法显著增加了重构图像的PSNR，而计算复杂度保持不变。
The compressive sensing(CS) theroy pointed out that for sparse or compressiblesignals, sampling rate is determined by the structure and content of information insignal rather than by the bandwidth of signal. Currently, much achievement has beenyielded in the research on CS theory and applications, while there are still many openproblems to be studied further. For the existing proplems,this disseration studied somekey issues as directional transform, feature dictionary, video analysis, compressiveimaging which are theoretically important and practically valuable. The maincontributions and innovations are as the following:
Firstly, the practice of directional-transforms method in CS construction of imagewas studied which using a general frame of projected-based reconstruction withblocked random sampling of images to improve sparsity and smoothness as well. Thisframework facilitated introducing of directional transforms based on contourlets anddual-tree complex wavelets into the CS reconstruction and finally led to the fastfunction speed of the projection-based CS reconstruction. Simultaneouly, thecombination of a smoothing step and boosted directionality naturally improved imagequality, particularly for the cases at low sampling rates.
Secondly, taking advantage of the sparsity of Hough transform, a sparsifyrepresentation dictionary of shapes was built which using CS method to search forparameterized shapes in images. An experiement on detecting lines and circles in annoisy image from a few CS measurements was implemented indicating that there’spossibility to get cleaner results than Hough transform. Furthermore, the analysis ofdetect rate v.s. SNR and detect rate v.s. number of measurements was conducted.
Thirdly, a privacy-protection video-monitoring encoding scheme was designedwhich was able to track an object without the need to reconstruct each original frame.Subsequently, this scheme ensures to encoding a video sequence by using a fewpesudo-random projections of each frame, while the decoder reconstructs the positionof foreground targets by exploiting the sparsity of background-subtracted images. Itworks with a particle filter in order to estimate the position of targets, then theestimated position in turn serves as a prior to promote the recovering of foreground.Privacy protection roots in that it is impossible to reconstruct the original content only with a coded random projection, meanwhile, security roots in that if there is no seedwhich creates random projection, it would never decode.
Last but not the least, CCM used DMD to efficiently scan2D or3D specimenand all the resulting data coming from a random collect of pin-hole illuminatedspecimen pixels, measured by a single photon detector after linear combination(projection). Compare this with the traditional methods of CM or PAM, CCM speaksfor itself for its capacity of simplifying the complexity of confocol imaging hardwareand optics by off load processing from data aqusition stage to software image recoverand getting more cost-effective. Besides, CCM also provides special opticalsectioning property of confocol imaging at reduced sampling rate.3D jointlyreconstruct approach fully utilized the correlation among3D slices to promote systemperformace. In a word,3D method significantly increased the PSNR of imageconstruction while kept the same computational complexity.
(1)研究了在图像的CS重构中使用方向变换。采用分块随机图像采样与基于投影的重构相结合的一般框架，不仅提高了稀疏性，也提高了光滑性。这个框架便于在CS重构过程中加入基于方向变换的Contourlets和双树复小波。得到的算法具有基于投影的CS重构的快速运算速度，而平滑步骤与增强的方向性相结合，有助于获得更好的图像质量，尤其是在低采样率时。
(2)利用Hough变换域的稀疏性，建立起形状的稀疏表示字典，用CS方法寻找图像中的参数化形状。进行了用CS方法从含有噪声的图像的少量测量中检测直线和圆等图形的实验。实验表明CS方法能够得到比Hough变换更干净的检测结果。分析了检测率与信噪比，检测率与测量数的关系。
(3)提出一个适合隐私保护的视频监控应用的编码方案，能够跟踪视频目标而不需要重构视频序列。该方案利用每帧有限数量的伪随机投影编码一个视频序列，解码器利用背景消除图像所具有的稀疏性并重构前景目标的位置。该方案采用粒子滤波器预测目标位置，再用估计的位置作为先验知识改进前景目标位置的重构。隐私保护体现在只采用编码的随机投影不可能重构原始视频内容，安全性体现在如果没有用来产生随机投影的种子，就无法解码。
(4)压缩感知共焦显微镜（CCM）用数字微镜阵列（DMD）高效扫描2D或3D标本，其测量的数据来自针孔照亮的标本像素的随机集合，线性组合（投影）之后用单个光电检测器和测量。与传统CM或PAM相比，CCM能够简化共焦成像的硬件和光学系统的复杂性，将处理从数据采集步骤转移到软件图像重构，降低了成像系统的成本。CCM还以降低的采样速率提供了共焦成像的独特光学切片性质。3D联合重构方法充分利用3D图像图层之间的相关性，进一步提高了系统性能。与2D逐层方法相比，这种3D方法显著增加了重构图像的PSNR，而计算复杂度保持不变。
The compressive sensing(CS) theroy pointed out that for sparse or compressiblesignals, sampling rate is determined by the structure and content of information insignal rather than by the bandwidth of signal. Currently, much achievement has beenyielded in the research on CS theory and applications, while there are still many openproblems to be studied further. For the existing proplems,this disseration studied somekey issues as directional transform, feature dictionary, video analysis, compressiveimaging which are theoretically important and practically valuable. The maincontributions and innovations are as the following:
Firstly, the practice of directional-transforms method in CS construction of imagewas studied which using a general frame of projected-based reconstruction withblocked random sampling of images to improve sparsity and smoothness as well. Thisframework facilitated introducing of directional transforms based on contourlets anddual-tree complex wavelets into the CS reconstruction and finally led to the fastfunction speed of the projection-based CS reconstruction. Simultaneouly, thecombination of a smoothing step and boosted directionality naturally improved imagequality, particularly for the cases at low sampling rates.
Secondly, taking advantage of the sparsity of Hough transform, a sparsifyrepresentation dictionary of shapes was built which using CS method to search forparameterized shapes in images. An experiement on detecting lines and circles in annoisy image from a few CS measurements was implemented indicating that there’spossibility to get cleaner results than Hough transform. Furthermore, the analysis ofdetect rate v.s. SNR and detect rate v.s. number of measurements was conducted.
Thirdly, a privacy-protection video-monitoring encoding scheme was designedwhich was able to track an object without the need to reconstruct each original frame.Subsequently, this scheme ensures to encoding a video sequence by using a fewpesudo-random projections of each frame, while the decoder reconstructs the positionof foreground targets by exploiting the sparsity of background-subtracted images. Itworks with a particle filter in order to estimate the position of targets, then theestimated position in turn serves as a prior to promote the recovering of foreground.Privacy protection roots in that it is impossible to reconstruct the original content only with a coded random projection, meanwhile, security roots in that if there is no seedwhich creates random projection, it would never decode.
Last but not the least, CCM used DMD to efficiently scan2D or3D specimenand all the resulting data coming from a random collect of pin-hole illuminatedspecimen pixels, measured by a single photon detector after linear combination(projection). Compare this with the traditional methods of CM or PAM, CCM speaksfor itself for its capacity of simplifying the complexity of confocol imaging hardwareand optics by off load processing from data aqusition stage to software image recoverand getting more cost-effective. Besides, CCM also provides special opticalsectioning property of confocol imaging at reduced sampling rate.3D jointlyreconstruct approach fully utilized the correlation among3D slices to promote systemperformace. In a word,3D method significantly increased the PSNR of imageconstruction while kept the same computational complexity.
引文
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