Abstract: The measurement matrix construction algorithm is one of important research direction in compressed sensing. A measurement matrix algorithm based on Logistic Chaos-Bernoulli sequence is proposed according to the pseudo-random property of chaos sequence. It uses the one-dimensional Logistic chaotic system to generate the chaotic sequence, the pseudo-random sequence with Bernoulli distribution is generated by the symbol function and the sequence is used to construct the measurement matrix. Simulation results show that, the proposed algorithm performs better than the Bernoulli random measurement matrix and the PSNR of construct signal is improved about 1~3 dB, and it is feasible and effective by numerical analysis after comparing with other types of measure matrix.

Key words: compressed sensing, measurement matrix, chaotic system, Bernoulli distribution

摘要： 测量矩阵的构造算法是压缩感知中重要的研究方向之一。提出一种基于Logistic混沌—贝努利序列（Chaos-Bernoulli）测量矩阵构造算法，该算法利用了混沌序列良好的伪随机性质，通过一维Logistic混沌系统产生混沌序列，再通过符号函数生成具有贝努利分布的伪随机序列从而构造出压缩感知测量矩阵。实验仿真结果表明，该算法优于贝努利随机测量矩阵，信号重构的峰值信噪比PSNR有1~3 dB的提高，并与其他类型的测量矩阵进行比较，数值分析结果证明该算法是可行有效的。

关键词: 压缩感知, 测量矩阵, 混沌系统, 贝努利分布