基于PSO和LM的信号稀疏分解快速算法

Fast algorithm of sparse signal decomposition based on PSO and LM

摘要:

传感矩阵和重建算法的性能分析和优化是目前压缩传感领域研究的热点。针对匹配追踪算法在信号稀疏分解中计算量巨大的难题，提出了一种交替使用粒子群算法和Levenberg Marquardt算法的混合智能算法来寻找最佳原子。首先利用粒子群算法得到群体最优解，再以该解作为LM算法的初值，交替使用两种算法，直至发现满意的最优解。数值分析表明，新算法克服了粒子群算法过早收敛于局部极值和LM算法依赖初值的问题，保证了求解的速度和精度。

Abstract:

Performance analysis and optimization of sensing matrix and reconstruction algorithm have become a hot research field in compressed sensing.Matching pursuit algorithm has a huge computational problem for sparse signal decomposition,so a hybrid intelligent algorithm of using alternately particle swarm optimization and Levenberg Marquardt has been put forth to find the best atom.Firstly,a group of optimal approximate solutions are obtained by the way of the particle swarm optimization.Taking these approximate solutions as the initial values,the particle swarm optimization and LM algorithm are alternately used until the satisfactory optimal solution is found at last.These findings indicate that the new algorithm overcomes premature convergence of particle swarm optimization,at the same time weakens its dependence on the initial conditions in the LM algorithm.It guarantees the speed and precision of the solving process.