基于过完备字典的非凸压缩感知理论与方法研究

发布时间：2018-07-26 18:29

【摘要】：压缩感知是一种全新的信号获取和处理框架,其理论和技术的发展将对数字信号的获取方式,分析技术和处理方法等研究领域及相关应用领域产生深远的影响。目前,压缩感知正从理论研究向实际的信号应用领域发展:处理的数据对象从具有简单的理想稀疏性信号转向广泛的具有复杂低维结构的实际信号;信号的稀疏表示从基于正交基和框架发展为基于结构化的冗余字典;研究重点从理论研究发展为对应用中实际信号的重构和处理。其中,根据应用需求建立结构化重构模型以及高效的重构算法是压缩感知从理论走向实践中最重要的环节,也是压缩感知应用研究的热点。本论文工作中,建立了分块策略下的基于过完备字典的图像非凸压缩感知框架,其中,对图像进行分块压缩观测,即对图像的每个大小相等的图像块使用相同的随机观测方式;构造了Ridgelet过完备字典,获得对任意图像块的稀疏表示;挖掘和利用图像块在Ridgelet过完备字典中的稀疏性和结构稀疏先验,设计了从图像块的压缩观测中获得图像准确估计的重构模型。在此框架下,针对压缩感知重构的本源问题,即0l范数约束的非凸优化问题,我们提出了基于自然计算优化算法和协同优化的重构思路,建立了能够有效求解包含了非凸稀疏先验以及多种结构先验约束的图像重构方法。论文的主要工作包括:(1)为了获得全局寻优意义下的非凸压缩感知重构,提出了基于自然计算优化算法的两阶段重构框架。在该框架的第一阶段,设计了一种遗传算法来获得一类图像块在方向上的最优原子组合;第二阶段在第一阶段结果的基础上,设计了一种克隆选择算法来搜索自适应于每个图像块的子字典,并获得每个图像块在尺度和位移等参数上的更优原子组合。该框架采用全局寻优的进化搜索策略,通过灵活多样的进化策略设计来实现零范数和图像结构先验约束下的图像分块压缩感知重构。该工作是自然计算优化方法在非凸压缩感知重构中的成功应用尝试,能够获得对图像较好的重构估计。(2)考虑到基于进化搜索策略的重构方法存在重构速度较慢的问题,提出了基于过完备字典的协同压缩感知重构,其主要思想是用匹配追踪方法的局部搜索和交迭优化策略代替进化搜索中的全局搜索策略。该方法利用了图像的自相似特性,设计了两种协同重构方式,用于在局部和非局部相似的图像块间进行重构信息的传递和交换。第一种协同方式利用一组相似图像块的观测向量来重构单个图像块,第二种协同方式则利用一组图像块的估计值来获得对单个图像块的更优估计。实验结果表明,所提出的方法可以有效减少采用基于进化搜索策略的重构方法的运行时间,在性能上超过了经典匹配追踪算法。(3)为了获得对图像块局部结构的更准确估计,并提升已有协同重构方法,提出了一种几何结构指导的协同重构方法。该方法根据过完备字典中原子结构与图像块结构的匹配关系,对图像块在字典中的稀疏表示系数施加块稀疏结构约束,并将这些约束与协同重构机制结合,分别设计了针对光滑,单方向和随机结构图像块的协同重构模式和重构策略。与已有的协同重构方法相比,结合了几何结构先验的协同重构方法能够有效改善图像局部结构估计,并在重构精度和速度上都有所提升。(4)为了结合和利用图像块基于过完备字典的方向结构先验来获得对图像及其局部结构的准确重构,提出了基于方向指导的字典及进化搜索的重构策略。其中设计和提出了一种利用Ridgelet过完备字典根据图像块的压缩观测判定图像块结构类型的解析方法,将图像块判定为光滑,单方向和多方向块中的一种,并对单方向和多方向块的方向结构进行估计。根据对图像块的结构估计,我们为光滑和单方向图像块构造了稀疏子字典,并设计了方向指导的进化搜索重构策略。该重构策略中,对光滑图像块采用单阶段的进化重构策略;对单方向和多方向图像块首先基于方向指导的结构稀疏模型进行重构,再采用进化搜索策略进行再次优化估计。与已有的两阶段进化重构策略相比,本重构策略能够获得更准确的方向结构估计,以及更高的重构速度。通过本工作,展示了基于进化搜索的优化方法在具有非凸稀疏约束及其他结构先验共同约束的优化问题中的应用前景。
[Abstract]:Compressed sensing is a new framework for signal acquisition and processing. The development of its theory and technology will have a profound impact on the research fields of digital signal acquisition, analysis technology and processing methods and related applications. At present, compression perception is developing from theoretical research to real signal application field: data object processing. From simple ideal sparsity signals to a wide range of practical signals with complex and low dimensional structures; sparse representations of signals are developed from based on orthogonal bases and frameworks to structured redundant dictionaries; the focus of research is developed from theoretical research to the reconstruction and processing of practical signals in applications. The most important part of compression perception from theory to practice is the most important part of compression perception from theory to practice, and also a hot spot in compressed sensing application research. In this paper, an image non convex compression frame based on overcomplete dictionary based on partitioned strategy is established, in which the image is divided into block compression observation, that is, to the image Each image block with equal size uses the same random observation method; constructs the Ridgelet overcomplete dictionary to obtain the sparse representation of any image block, and uses the sparsity and the sparse priori in the Ridgelet overcomplete dictionary to excavate and make use of the image block in the overcomplete dictionary of the image. In this framework, in view of the source problem of compressed sensing reconstruction, that is, the non convex optimization problem of 0l norm constraint, we propose a reconstruction idea based on the natural computing optimization algorithm and the cooperative optimization, and establish an image reconstruction method which can effectively solve the non convex sparse prior and a variety of structure prior constraints. The work includes: (1) in order to obtain the non convex compression perception reconstruction under the global optimization, a two phase reconstruction framework based on the natural computing optimization algorithm is proposed. In the first stage of the framework, a genetic algorithm is designed to obtain the optimal combination of a class of image blocks in the direction; the second stage is based on the first stage result. A clonal selection algorithm is designed to search the sub dictionaries adaptive to each image block and obtain better atomic combinations of each image block on the parameters of scale and displacement. The framework uses a global optimization evolutionary search strategy to achieve zero norm and image structure prior constraints by a flexible and diverse evolutionary strategy design. This work is a successful application of natural computing optimization method in non convex compression sensing reconstruction, which can obtain better reconstruction estimation for images. (2) considering the problem of slow reconstruction in the reconstruction method based on evolutionary search strategy, a cooperative compression perception based on overcomplete dictionary is proposed. The main idea is to replace the global search strategy in the evolutionary search with the local search and overlapping optimization strategy of matching pursuit method. The method uses the self similarity of the image, and designs two cooperative reconfiguration methods for the transfer and exchange of the reconstruction information between the local and non local similar image blocks. In the same way, an observation vector of a group of similar image blocks is used to reconstruct a single image block. The second cooperative methods use an estimated value of a block of image blocks to obtain a better estimate of a single image block. The experimental results show that the proposed method can effectively reduce the running time of the reconfiguration method based on the evolutionary search strategy. 3. (3) in order to obtain more accurate estimation of the local structure of the image block, and to improve the existing cooperative reconfiguration method, a collaborative reconstruction method guided by geometric structure is proposed. The representation coefficient applies the block sparse structure constraint, and combines these constraints with the cooperative reconfiguration mechanism, designs the cooperative reconstruction mode and reconfiguration strategy for smooth, single direction and random structure image blocks respectively. Compared with the existing cooperative reconstruction method, the cooperative reconstruction method combining the geometric structure first test can effectively improve the image part. The structure estimation and the reconstruction precision and speed have been improved. (4) in order to combine and utilize the image block based on the direction structure prior to the overcomplete dictionary, the accurate reconstruction of the image and its local structure is obtained. A dictionary based on direction guidance and the reconstruction strategy of evolutionary search are proposed, in which a kind of use of Ridgelet is designed and proposed. An overcomplete dictionary determines the structure type of the block according to the compression observation of the image block. The image block is determined as one of the smooth, single and multi direction blocks, and the direction structure of the single direction and multi direction block is estimated. According to the structure estimation of the image block, we construct the sparsity for the smooth and single direction image blocks. An evolutionary search reconfiguration strategy directed by direction is designed. In this reconfiguration strategy, a single stage evolutionary reconfiguration strategy is adopted for smooth image blocks; a single directional and multi direction image block is restructured in the first direction based structural sparse model, and then the evolutionary search strategy is used for the reoptimization estimation. The two phase of the reconfiguration is made with the existing evolutionary search strategy. Compared with the evolutionary reconstruction strategy, this reconfiguration strategy can obtain more accurate direction structure estimation and higher reconstruction speed. Through this work, the optimization method based on evolutionary search is shown to be applied in the optimization problem with non convex sparse constraints and other structural priori constraints.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41

【相似文献】