Jiang Lanfan, Zhu Wenxing
IEEE Trans Neural Netw Learn Syst. 2021 Jan;32(1):63-76. doi: 10.1109/TNNLS.2020.2975302. Epub 2021 Jan 4.
This article proposes a novel iterative weighted group thresholding method for group sparse recovery of signals from underdetermined linear systems. Based on an equivalent weighted group minimization problem with l -norm ( ), we derive closed-form solutions for a subproblem with respect to some specific values of p when using the proximal gradient method. Then, we design the corresponding algorithmic framework, including stopping criterion and the method of nonmonotone line search, and prove that the solution sequence generated by the proposed algorithm converges under some mild conditions. Moreover, based on the proposed algorithm, we develop a homotopy algorithm with an adaptively updated group threshold. Extensive computational experiments on the simulated and real data show that our approach is competitive with state-of-the-art methods in terms of exact group selection, estimation accuracy, and computation time.
本文提出了一种新颖的迭代加权组阈值方法，用于从不确定线性系统中对信号进行组稀疏恢复。基于一个具有l -范数（ ）的等效加权组最小化问题，我们在使用近端梯度法时针对p的某些特定值推导了子问题的闭式解。然后，我们设计了相应的算法框架，包括停止准则和非单调线搜索方法，并证明了所提算法生成的解序列在一些温和条件下收敛。此外，基于所提算法，我们开发了一种具有自适应更新组阈值的同伦算法。在模拟数据和真实数据上进行的大量计算实验表明，我们的方法在精确组选择、估计精度和计算时间方面与现有方法具有竞争力。
