Abstract
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.
Highlights
The compressed sensing technology [1], [2] has been widely applied to many fields, such as medical imaging [3], [4] [5], face recognition, radar and sensor networks, and seismic data reconstruction [6], [7]
Based on the decomposition idea, we propose a localized regularization strategy to improve the local search efficiency, i.e., different regularization values are restricted to work within the local search of the solutions to different decomposed subproblems
We propose a localized regularization strategy, in which an independent regularization value is assigned to each subpopulation, and this value can be determined by using the preference of the corresponding subproblem over the two objectives as a priori
Summary
The compressed sensing technology [1], [2] has been widely applied to many fields, such as medical imaging [3], [4] [5], face recognition, radar and sensor networks, and seismic data reconstruction [6], [7]. The proposed knowledge transfer operator is implemented to obtain a set of sparsified knowledge-induced solutions Tt , and the solutions from Tt and Pt are used to integrate the learned search experience from the source problem into the evolution of the target problem via the simulated binary crossover (line 610 of Algorithm 2). 3) SPARSE CONSTRAINT To ensure the sparsity characteristics of solutions in Zt , we combine the sparse structure of Pt into Zt to obtain the sparse version of Zt , Tt. As a result, Tt will possess the valuable knowledge extracted from the search experience for the target problem, and inherit the sparse structure of Pt. In detail, firstly, we identify the positions of zero elements in Pt , and form a set Z {z|[Pt ]i,z = 0}, where [·]i,z represents the (i, z)-th element in a matrix.
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