ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2019, Vol. 56 ›› Issue (7): 1420-1431.

### Multi-Objective Evolutionary Sparse Recovery Approach Based on Adaptive Local Search

Liu Haolin1,2, Chi Jinlong1, Deng Qingyong1,2, Peng Xin3, Pei Tingrui1,2

1. 1(College of Information Engineering, Xiangtan University, Xiangtan, Hunan 411105);2(Key Laboratory of Hunan Province for Internet of Things and Information Security (Xiangtan University), Xiangtan, Hunan 411105);3(School of Information Science and Engineering, Hunan Institute of Science and Technology, Yueyang, Hunan 414000)
• Online:2019-07-01

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.

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