基于改进遗传算法的稀疏重构算法

稀疏重构算法中凸松弛法在恢复效率方面、贪婪追踪法在恢复精度方面存在不足，基于遗传算法迭代优化的思想，结合模拟退火以及多种群算法的优势，提出了基于模拟退火遗传算法和基于多种群遗传算法的启发式稀疏重构算法。所提算法均从传统遗传算法易陷入局部最优解的缺陷出发，分别通过保持个体间的差异性和提高种群多样性来搜索待求稀疏信号的全局最优解，并通过理论分析证明了所提算法参数选取及搜索策略的有效性。此外，以阵列信号处理中空间信源的波达方向（DOA）估计问题为例，验证所提算法的有效性。仿真结果表明，相较于正交匹配追踪OMP算法和基于l1范数奇异值分解的l1-SVD算法，所提算法提高了DOA估计的精度，且降低了运算复杂度，使其快速收敛至全局最优解。

Sparse reconstruction algorithm based on improved genetic algorithm

Convex relaxation methods present drawback in terms of computational complexity, meanwhile, greedy pursuit methods have disadvantages in their reconstruction accuracy. Based on the inspiration of iterative optimization of genetic algorithm and combining with the advantages of simulated annealing and multi-population algorithm, this paper proposed two heuristic sparse reconstruction algorithms based on simulated annealing genetic algorithm and multi-population genetic algorithm. Aiming at the defects of the traditional genetic algorithm that often trapped in the local optimal solutions, it implemented two strategies to search global optimal solutions of the sparse reconstruction via maintaining the differences among individuals and increasing the diversity of the population, respectively. The validity of the proposed algorithms on parameters selection and search strategy was proved by theoretical analysis. The proposed algorithms could be applied to the DOA estimation of multiple spatial sources in array signal processing to verify the effectiveness. Simulation results show that, compared with the OMP algorithm and l1-SVD algorithm, the proposed algorithms have improved the accuracy and reduced the computational complexity, which can converge to the global optimal solution in a fast manner.