Discrete-Valued Vector Reconstruction by Optimization with Sum of Sparse Regularizers
Discrete-Valued Vector Reconstruction by Optimization with Sum of Sparse Regularizers
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DOI：
10.23919/eusipco.2019.8902940
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发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
Ryo Hayakawa;K. Hayashi
中科院分区：
文献类型：
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作者：
Ryo Hayakawa;K. Hayashi
在这篇文章中，我们提出了一个可能的非凸优化问题，从它的欠定线性测量重构一个离散值向量。所提出的稀疏正则化子之和(SSR)优化使用稀疏正则化子之和作为离散值向量的正则化。在乘子交替方向法(ADMM)和原始-对偶分裂法(PDS)的基础上，提出了求解SSR优化问题的两种近似分裂算法。基于ADMM的算法可以达到更快的收敛速度，而基于PDS的算法不需要计算任何矩阵的逆。此外，我们还扩展了基于ADMM的复离散值向量重构方法。值得注意的是，所提出的方法可以使用任何稀疏正则化，只要其邻近算子能够被有效地计算。仿真结果表明，基于非凸正则的重建算法具有较好的重建性能。
In this paper, we propose a possibly nonconvex optimization problem to reconstruct a discrete-valued vector from its underdetermined linear measurements. The proposed sum of sparse regularizers (SSR) optimization uses the sum of sparse regularizers as a regularizer for the discrete-valued vector. We also propose two proximal splitting algorithms for the SSR optimization problem on the basis of alternating direction method of multipliers (ADMM) and primal-dual splitting (PDS). The ADMM based algorithm can achieve faster convergence, whereas the PDS based algorithm does not require the computation of any inverse matrix. Moreover, we extend the ADMM based approach for the reconstruction of complex discrete-valued vectors. Note that the proposed approach can use any sparse regularizer as long as its proximity operator can be efficiently computed. Simulation results show that the proposed algorithms with nonconvex regularizers can achieve good reconstruction performance.