帐篷混沌序列稀疏测量矩阵构造

Construction of sparse measurement matrix via tent chaotic sequence

测量矩阵的构造是压缩感知(CS)中重要的研究内容之一。利用混沌系统伪随机性、遍历性的特点,提出了一种基于帐篷混沌序列构造确定性稀疏随机矩阵的方法。对混沌系统生成的确定性序列进行了间隔采样,采样后的序列满足统计独立性,然后通过符号函数映射,生成了具有稀疏性质的伪随机序列,进而构造出混沌稀疏测量矩阵。仿真实验表明:该方法构造出的混沌稀疏测量矩阵与高斯随机矩阵、稀疏随机矩阵及Bernoulli随机矩阵相比,具有类似的重构性能。混沌系统参数与初值固定时,构造的混沌稀疏测量矩阵是确定的,计算复杂度小且硬件上容易实现。

Construction of measurement matrix is one of the important research content in compressed sensing （CS）. Using characteristic of pseudo randomness, ergodicity of chaotic systems,propose a method for construction of the sparse measurement matrix based on tent chaotic sequence. The method for deterministic chaotic sequence generated by the system will be interval sampling, so that the sampled sequence meet statistical independence, by symbol function mapping generate pseudo-random sequence having sparsity, thereby construct measurement matrix of chaotic sparse. Simulation experiments results show that compared with Gaussian random matrices, sparse random matrix and Bernoulli random matrix, this proposed matrix has a similar reconstruction performance. The proposed measurement matrix is deterministic when parameter of chaotic system and initial value are fixed, its computation complexity is small and it is easy to be realized by hardware.