【摘要】 在压缩感知理论的稀疏表示过程中,通常选择正交完备字典实现信号稀疏表示.冗余字典比完备字典表现出对信号更好的适应性,常见的冗余字典直接由两个或多个正交完备字典级联而成.为了设计对信号具有更好适应性的冗余字典,改变原有正交完备字典,通过对正交傅里叶完备字典中的原子进行扩展、延时、混叠等一系列变换,设计出一种新的非正交完备字典.在此基础上,将该完备字典与单位矩阵级联构造了新的非正交冗余字典.以一维信号作为测试信号,研究了冗余字典的性能.仿真实验结果表明提出的非正交冗余字典比正交傅里叶完备字典具有更好的稀疏性能和重构性能.更多还原

【Abstract】 In the sparse representation of compressed sensing(CS)theory,orthogonal complete dictionary is usually utilized to accomplish the process of signal sparse representation.The redundant dictionary,jointed by two or multiple orthogonal complete dictionaries commonly,shows better adaptability to signals than the complete dictionary.In order to improve the adaptability of redundant dictionary further,some changes on the orthogonal complete dictionary was made.A new non-orthogonal complete dictionary was designed through extending,aliasing and delaying on the elements of the orthogonal Fourier dictionary.Besides,a non-orthogonal redundant dictionary was constructed,which jointed a unit matrix with the non-orthogonal complete dictionary designed.The performance of the nonorthogonal redundant dictionary proposed in this paper was analyzed by taking one-dimensional signal as the test signal.Simulation results show that the constructed non-orthogonal redundant dictionary has much better performance in sparse representation and recovery of the test signal than orthogonal Fourier complete dictionary.更多还原