基于原子库树状结构划分的诱导式信号稀疏分解

针对以往提出的稀疏分解算法仅从原子库构造方面或分解方式角度对算法进行各种改进且计算复杂度高的问题,提出了一种诱导性塔式分解算法.该算法首先将原子库逐层划分,得到一个树状层次结构的原子库,然后在迭代过程中利用划分所得树状结构有目的、有导向性地指引信号分解方向,从而一劳永逸地加快了信号分解速度,极大地降低了算法的计算复杂度.实验结果表明,与经典的匹配追踪(matching pursuit,MP)算法相比,本文算法在同等稀疏度且逼近误差接近的情况下,计算量大约降低为MP算法的1/40,计算时间降低为MP算法的1/100左右.仿真实验证明了该算法的有效性.

Guiding method of signal sparse decomposition based on tree-structured partition of atom dictionary

To overcome the deficiency of traditional sparse decomposition algorithm,in which the performance improvement is merely made either by improving the mode of constructing atom dictionary or by decomposing method,and it also has a high calculative complexity,a new guiding pyramidal algorithm of sparse decomposition is presented.The algorithm firstly divides the atom dictionary into several subsets by its characteristics and forms a tree structure atom dictionary after several layer-by-layer partition of the atom set.Then the decomposing of signals can be purposefully performed along the course charted by the tree structure at each iteration and the decomposing speed is greatly increased,and the calculative complexity is sharply decreased.Experiment results show that the calculating amount of the new algorithm is only about 1/40 of MP algorithm,and the computing time 1/100 of MP algorithm,under the condition of the same sparsity and similar approximation error.The simulation results indicate that the presented method is efficient.