论文标题
基于模型的神经网络及其在线光谱估计中的应用
Model-Based Neural Network and Its Application to Line Spectral Estimation
论文作者
论文摘要
本文介绍了“基于模型的神经网络”（MNN）的概念，该概念受到经典人工神经网络（ANN）的启发，但用于不同的用法。 MNN不是被用作数据驱动的分类器，而是具有具有明确物理含义的巧妙定义输入，输出和激活功能的建模工具。由于与ANN相同的分层形式，也可以使用后传播（BP）算法优化MNN。作为一个有趣的应用，可以通过MNN对线频谱估计的经典问题进行建模。我们建议首先通过基于快速傅立叶变换（FFT）的光谱估计初始化MNN，然后通过BP算法优化MNN，该算法会自动产生频谱的最大似然（ML）参数估计。我们还设计了一种合并和修剪MNN的隐藏层节点的方法，该节点可用于模型订单选择，即估计正弦曲线的数量。数值模拟验证了所提出的方法的有效性。
This paper presents the concept of "model-based neural network"(MNN), which is inspired by the classic artificial neural network (ANN) but for different usages. Instead of being used as a data-driven classifier, a MNN serves as a modeling tool with artfully defined inputs, outputs, and activation functions which have explicit physical meanings. Owing to the same layered form as an ANN, a MNN can also be optimized using the back-propagation (BP) algorithm. As an interesting application, the classic problem of line spectral estimation can be modeled by a MNN. We propose to first initialize the MNN by the fast Fourier transform (FFT) based spectral estimation, and then optimize the MNN by the BP algorithm, which automatically yields the maximum likelihood (ML) parameter estimation of the frequency spectrum. We also design a method of merging and pruning the hidden-layer nodes of the MNN, which can be used for model-order selection, i.e., to estimate the number of sinusoids. Numerical simulations verify the effectiveness of the proposed method.
