基于自适应感知字典的块稀疏信号重建理论与方法研究

The difficulty and bottleneck of recovery performance of the existing algorithms by using sparse representation and compressed sensing method is breaking through the limits of block coherence to the algorithms for block-sparse signals recovery. To solve the problem of the limitation of block coherence to the existing algorithm, a sensing dictionary will be introduced in this project try to reveal the mechanism of interference suppressing for block coherence and to fulfill the recovery theories of block-sparse signals. We will obtain the posterior knowledge from the observed data, construct the adaptive sensing dictionary and make a further exploration on the new methods of block-sparse signals to improve the recovery performance. Research findings can solve the problem that the existing algorithms for block-sparse signals can't be used for high redundant dictionaries, and also solve the problem that the existing algorithms can't break through the Block Restricted Isometry Property in compressed sensing of block-sparse signals recovery. Therefore, our researches can provide theoretical bases and technical supports for more effective utilization of sparsity to feature extraction and data compression.

突破块相干对块稀疏重建算法的限制是当前稀疏表示和压缩感知进一步提高算法重建性能的难点和瓶颈。本项目针对现有的块稀疏重建算法受到块相干限制的问题，采用引入感知字典的方法，揭示抑制块稀疏重建算法中块相干影响的机制，发展基于感知字典的块稀疏信号重建理论；利用观测数据提取有效的后验信息，构造自适应感知字典，进而探索提高块稀疏信号重建性能的新方法。本项目的研究成果可解决现有的块稀疏重建算法无法用于高度冗余超完备字典的问题，也可解决现有的压缩感知重建算法无法突破块有限等距性质限制的问题，为更有效地利用稀疏性进行特征提取或数据压缩提供理论依据和技术支持。

本项目研究了基于自适应感知字典的块稀疏信号重构问题，构造了自适应感知字典，对现有的OMP和BOMP等稀疏重构算法进行修正，提高这些算法的重建性能，并推广应用到块相关性较强的情况。主要的研究内容包括：（1）推导了基于感知字典的块稀疏算法重构条件；（2）基于交替投影算法和重加权迭代提出了感知字典构造方法；（3）研究了基于自适应感知字典的块稀疏重构性能；（4）研究了存在噪声情况下的自适应块稀疏重建算法。