【摘要】：針對(duì)常用隨機(jī)測(cè)量矩陣存在硬件實(shí)現(xiàn)困難的不足,提出一種基于復(fù)合混沌映射的壓縮感知確定性測(cè)量矩陣構(gòu)造方法.首先基于Logistic映射和Tent映射構(gòu)造隨機(jī)性和初值敏感性更強(qiáng)的復(fù)合混沌映射,然后將復(fù)合混沌迭代序列經(jīng)大間隔采樣后進(jìn)行線性變換得到的結(jié)果作為擬構(gòu)造測(cè)量矩陣中的元素,并從理論上證明了該矩陣元素具有非常低的相關(guān)性.同時(shí)理論證明了所構(gòu)造復(fù)合混沌測(cè)量矩陣能以高概率滿足壓縮感知約束等距性.實(shí)驗(yàn)結(jié)果表明,所構(gòu)造復(fù)合混沌測(cè)量矩陣的性能優(yōu)于Toeplitz測(cè)量矩陣及Logistic映射測(cè)量矩陣,與高斯隨機(jī)測(cè)量矩陣的性能相仿.
[Abstract]:In order to overcome the difficulties in hardware implementation of random measurement matrices, a method of constructing a compressed perceptual deterministic measurement matrix based on complex chaotic mapping is proposed. Based on Logistic map and Tent map, a complex chaotic map with more randomness and sensitivity to initial value is constructed, and then the result obtained by linear transformation of the iterative sequence of composite chaos after sampling at large intervals is regarded as the element in the quasi-constructed measurement matrix. It is proved theoretically that the matrix element has very low correlation. At the same time, it is proved theoretically that the constructed composite chaotic measurement matrix can satisfy the isometry of compressed perceptual constraints with high probability. The experimental results show that the performance of the constructed composite chaotic measurement matrix is superior to that of the Toeplitz measurement matrix and the Logistic mapping measurement matrix, which is similar to that of Gao Si random measurement matrix.
【作者單位】： 空軍工程大學(xué)航空航天工程學(xué)院;北京機(jī)電工程研究所;
【分類號(hào)】：O151.21

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