信号稀疏分解中过完备原子库的集合划分

信号稀疏分解中使用的过完备原子库对分解效果十分重要,但同时它也是造成稀疏分解计算非常复杂的关键因素。为此,本文提出了利用信号集合划分研究过完备原子库的新方法。利用原子之间的等价关系,可以把过完备原子库划分成互不相交的子库,而每一个原子子库只需要用一个选出的相对应的原子即可代表。利用过完备原子库的集合划分,在信号稀疏分解效果不变的条件下,可以使信号稀疏分解过程的计算复杂度大为降低。本文所提方法的可行性和有效性为实验结果所证实。

Set Partitioning of the Over-complete Dictionary in Signal Sparse Decomposition

The over-complete dictionary of atoms is very important to the signal sparse decomposition results,and it is also the main reason for the high computational complexity in sparse decomposition.To reduce this high computational complexity,a new method is proposed to deal with the over-complete dictionary based on the signal set partitioning method.With the equalvalent relationship,the over-complete dictionary can be partitioned into sub-dictionaries,the intersections of which are null.Each sub-dictionary can then be represented by only one selected corresponding atom.By partitioning the over-complete dictionary,the computational complexity in signal sparse decomposition can be degraded a lot,while the decomposition results are kept unchanged.Finally the experimental results verify the feasibility and efficiency of the proposed method.