基于自适应感知字典的块稀疏信号重建理论与方法研究

项目名称： 基于自适应感知字典的块稀疏信号重建理论与方法研究

项目编号： No.61261048

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 无线电电子学、电信技术

项目作者： 黄安民

作者单位： 井冈山大学

项目金额： 40万元

中文摘要： 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。

中文关键词： 块稀疏信号；稀疏重构；感知字典；交替投影；重加权迭代算法

英文摘要： 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.

英文关键词： Block-sparse signals；Sparse reconstruction；Sensing dictionary；Alternative projection；Re-weighted iterative algorithm