Model-Based Neural Network and Its Application to Line Spectral Estimation

TL;DR

This paper introduces a model-based neural network (MNN) framework for line spectral estimation, combining physical modeling with neural network optimization to improve parameter estimation and model order selection.

Contribution

It proposes a novel MNN approach for spectral estimation, initialized with FFT and optimized via back-propagation, enabling automatic maximum likelihood estimation and model order determination.

Findings

MNN achieves accurate spectral parameter estimation.

The method effectively estimates the number of sinusoids.

Numerical simulations confirm the approach's effectiveness.

Abstract

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.