  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.
