Multi-Objective Sparse Reconstruction With Transfer Learning and Localized Regularization

Multi-objective sparse reconstruction methods have shown strong potential in sparse reconstruction. However, most methods are computationally expensive due to the requirement of excessive functional evaluations. Most of these methods adopt arbitrary regularization values for iterative thresholding-based local search, which hardly produces high-precision solutions stably. In this article, we propose a multi-objective sparse reconstruction scheme with novel techniques of transfer learning and localized regularization. Firstly, we design a knowledge transfer operator to reuse the search experience from previously solved homogeneous or heterogeneous sparse reconstruction problems, which can significantly accelerate the convergence and improve the reconstruction quality. Secondly, we develop a localized regularization strategy for iterative thresholding-based local search, which uses systematically designed independent regularization values according to decomposed subproblems. The strategy can lead to improved reconstruction accuracy. Therefore, our proposed scheme is more computationally efficient and accurate, compared to existing multi-objective sparse reconstruction methods. This is validated by extensive experiments on simulated signals and benchmark problems.