In this paper, it is proposed the directional estimation model on the overcomplete dictionary, which bridges the compressed measurements of the image blocks and the directional structures of the dictionary. In the model, it is established the analytical method to estimate the structure type of a block as either smooth, single-oriented, or multioriented. Furthermore, the structures of each type of blocks are described by the structured subdictionaries. Then based on the obtained estimations and the constrains on the sparse dictionaries, the original image will be estimated. To verify the model, the nonconvex methods are designed for compressed sensing. Specifically, the greedy pursuit-based methods are established to search the subdictionaries obtained by the model, which achieve better local structural estimation than the methods without the directional estimation. More importantly, it is proposed the nonconvex image reconstruction method with direction-guided dictionaries and evolutionary searching strategies (NR_DG), where the evolutionary searching strategies are delicately designed for each type of the blocks based on the directional estimation. By the experimental results, it is shown that the NR_DG method performs better than the available two-stage evolutionary reconstruction method.

中文翻译：

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基于超完备字典的方向估计模型和非凸重构方法


本文提出了过完备字典的方向估计模型，将图像块的压缩测量和字典的方向结构联系起来。模型中建立了解析方法来估计块体的结构类型是光滑的、单向的还是多向的。此外，每种类型的块的结构由结构化子词典描述。然后根据获得的估计和稀疏字典的约束，对原始图像进行估计。为了验证模型，非凸方法被设计用于压缩感知。具体来说，建立了基于贪婪追踪的方法来搜索模型获得的子词典，该方法比没有方向估计的方法获得了更好的局部结构估计。更重要的是，提出了带有方向引导字典和进化搜索策略的非凸图像重建方法（NR_DG），其中基于方向估计为每种类型的块精心设计了进化搜索策略。实验结果表明，NR_DG方法比现有的两阶段进化重建方法表现更好。