基于子空间的三阶多项式相位信号快速稀疏分解算法

针对稀疏分解冗余字典中原子数量庞大的缺点，该文提出一种三阶多项式相位信号的快速稀疏分解算法。该算法根据三阶多项式相位信号的特点，把原有信号变换成两个子空间信号，并根据这两个子空间信号构建相应的冗余字典，然后采用正交匹配追踪法来完成其稀疏分解，最后利用稀疏分解原理完成原有信号的稀疏分解。该算法把原有信号变换成两个不同子空间信号，构建了两个不同的冗余字典，对比采用一个冗余字典库，这种采用两个冗余字典的算法大大减少了原子数量，并且通过快速傅里叶变换，在一个冗余字典进行稀疏分解时，同时找到另一个冗余字典中的最匹配的原子。因此该算法通过减少原子数量和采用快速傅里叶变换大大加快了稀疏分解速度。实验结果表明，相比于采用Gabor原子构建的冗余字典，采用匹配追踪算法与遗传算法及最近提出的基于调制相关划分的快速稀疏分解，它的稀疏分解速度更快，并且具有更好的收敛性。

A Fast Sparse Decomposition for Three-order Polynomial Phase Signal Based on Subspace

In view of the defect for large number of atoms in the over-complete dictionary during sparse decomposition, this paper presents a fast sparse decomposition algorithm for three-order polynomial phase signal based on subspace. According to the characteristic of three-order polynomial phase signal, the original signal is transformed into two subspace signals, then the atoms are structured based on the two subspace signals in the over-complete dictionary, and the two subspace signals are sparsely decomposed by using orthogonal matching pursuit algorithm. Finally, the sparse decomposition for the original signal is completed by using the theory of the sparse decomposition. In the algorithm, three-order polynomial phase signal is transformed into two subspace signals, and two over-complete dictionaries are structured based on the two subspace signals. Compared to one over-complete dictionary, the atoms are reduced enormously by using two over-complete dictionaries in the algorithm, and one matching atom can be obtained in one over-complete dictionary when another matching atom in another over-complete dictionary is obtained by using fast Fourier transform. Therefore the method can sparsely decompose three-order polynomial phase signal with low computational complexity by reducing the atoms and using fast Fourier transform. Simulation results show that the computational efficiency of the proposed method is better than that of using Gabor atoms, genetic algorithm and the algorithm based on modulation correlation partition, and the sparsity is better.