IEEE Trans Cybern. 2021 Aug;51(8):4327-4336. doi: 10.1109/TCYB.2019.2925707. Epub 2021 Aug 4.
The fused lasso signal approximator (FLSA) is a vital optimization problem with extensive applications in signal processing and biomedical engineering. However, the optimization problem is difficult to solve since it is both nonsmooth and nonseparable. The existing numerical solutions implicate the use of several auxiliary variables in order to deal with the nondifferentiable penalty. Thus, the resulting algorithms are both time- and memory-inefficient. This paper proposes a compact neural network to solve the FLSA. The neural network has a one-layer structure with the number of neurons proportionate to the dimension of the given signal, thanks to the utilization of consecutive projections. The proposed neural network is stable in the Lyapunov sense and is guaranteed to converge globally to the optimal solution of the FLSA. Experiments on several applications from signal processing and biomedical engineering confirm the reasonable performance of the proposed neural network.
融合套索信号逼近器（FLSA）是一个重要的优化问题，在信号处理和生物医学工程中有广泛的应用。然而，由于该优化问题是非光滑和不可分离的，因此很难求解。现有的数值解需要使用多个辅助变量来处理不可微的惩罚项。因此，所得到的算法在时间和内存效率上都不高。本文提出了一种紧凑的神经网络来解决 FLSA 问题。该神经网络具有一层结构，神经元的数量与给定信号的维数成正比，这要归功于连续投影的使用。所提出的神经网络在李雅普诺夫意义上是稳定的，并保证全局收敛到 FLSA 的最优解。来自信号处理和生物医学工程的几个应用的实验证实了所提出的神经网络的合理性能。
