基于线性化的混沌压缩感知重构算法

随着信号的数据量和带宽不断增长，压缩感知作为一种新的信号低速率获取理论迅速成为信号处理界的热点。目前，压缩感知一般采用线性测量方式。混沌压缩感知是一种利用混沌系统实现非线性测量，非线性等式约束L1范数最小化实现信号重构的压缩感知理论；具有实现结构简单，测量数据保密性强等特点。但是，现有算法不能有效地求解非线性等式约束L1范数最小化，求解结果受到额外参数影响。该文通过对非线性约束线性化处理，将非线性等式约束L1范数最小化问题转化为一系列二次锥规划问题，利用线性化迭代二次锥规划算法进行求解，保证了算法的收敛性和提高了信号的重构性能。本文以Henon混沌为例，研究了频域稀疏信号的重构性能，数值模拟证明了该算法的有效性。 

Linearization based Reconstruction Algorithm of Chaotic Compressive Sensing

With persistently increased data and bandwidth of signal, compressive sensing as a new low rate sampling method rapidly becomes a hotspot in signal processing society. Recently, compressive sensing usually measures the signal by linear manner. Chaotic Compressive Sensing (ChaCS) is a nonlinear compressive sensing theory which uses chaos systems to measure signals and performs the signal reconstruction by nonlinearly constrained L1-norm minimization. ChaCS is simple in implementation and generates secure measurement data. However, existing algorithms cannot efficiently solve the nonlinearly constrained L1-norm minimization, and the reconstruction quality is affected by the extra algorithm parameters. By linearization of nonlinear constraints, this paper proposes to solve the problem by iterative second order cone programming through the transformation of the nonlinearly constrained L1-norm minimization into a series of second order cone programming. The resulting algorithm is convergent and improves the reconstruction performance of signals. The Henon system is taken as examples to expose the estimation performance of frequency sparse signals. Numerical simulations illustrate the effectiveness of the proposed method.