摘要:
在稀疏重构中,重构误差项和稀疏项通常使用一个正则化参数聚合成单目标函数,很难实现2个目标的均衡优化,这个缺陷通常导致稀疏重构精度低.为此,提出一种自适应局部搜索的多目标进化算法.首先,基于范数和l\-1范数和l\-{1/2}范数分别设计了2种梯度迭代软阈值法的局部搜索方法求得相应解,这2种局部搜索方法可以提高解的收敛速度和精确度;其次,通过比较对应的目标函数值来竞争选取每轮的优胜解;然后,采用基于竞争成功率的自适应择优局部搜索方法来产生后期解;最后,在帕雷托前沿面的膝盖区域上采用角度法选取最优解.实验结果表明:测量误差和稀疏项可以达到平衡,在重构精度方面,提出的方法远高于现有的传统单目标方法.相比于StEMO算法,当测量维度M=600时,该方法可以提高33.8%;当噪声强度δ=0.002时可以提高82.7%;当稀疏率K/N=0.3时可以提高7.38%.
Abstract:
In sparse recovery, a regularization parameter is usually introduced to aggregate the measurement error term and the sparsity term into a single function, but it is hard to balance them, and this weakness usually leads to low precision of sparse recovery. To solve this problem, a new evolutionary multi-objective approach based on adaptive local search method is proposed in this paper. First, two gradient iterative soft thresholding local search methods based on l\-1 norm and l\-{1/2} norm are designed to obtain corresponding solutions, and they can improve the convergence speed and accuracy of the solutions. Second, the winner solution is selected by comparing the corresponding objective function values in each round. Then, based on the competition success rate, the winner local search method is chosen adaptively to generate latter solutions. Finally, the optimal solution is derived by the angle-based method on the keen region of Pareto front. Experiments show that the measurement error and the sparsity terms can be balanced and our proposed method gains an advantage over the other eight single objective algorithms in terms of recovery accuracy. Compared with the StEMO algorithm, our approach can improve more than 33.8% when the measurement dimension M=600, 82.7% when the noise intensity δ=0.002, and 7.38% when the sparsity ratio K/N=0.3.
百度学术
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