基于联合过完备库的信号分离及重构

在信号稀疏分解理论的基础上，提出了构建联合过完备库的思想。通过对包含不同特征成分的过完备子库进行联合构建联合过完备库，它包含丰富的待分解信号的信息，复合信号在其上具有更好的稀疏性，同时由于每个分量信号在各自的过完备子库上均具有稀疏性，利用基追踪算法实现各个分量信号的分离和重构。仿真结果表明：联合过完备库对复合信号的重构以及分量信号的分离和重构具有较好地效果。

Signal Separation and Reconstruction over Combined Over-complete Dictionary

The combined over-complete dictionary is proposed based on the theory of sparse decomposition to achieve signal separation and reconstruction which is intensively studied and has been widely applied to many areas in signal processing. The combined over-complete dictionary is composed of many over-complete dictionaries with single feature, contains enough information of decomposed signal and makes complex signal more sparse, so separate signals can be separated and reconstructed much better by the basis pursuit algorithm. The simulation results show that the proposed idea of the combined over-complete dictionary is efficient to the complex signal reconstruction and separate signal separation and reconstruction.