Neural Network for Direct and Inverse Nonlinear Fourier Transform
Date:
We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct and inverse spectral problem associated with the nonlinear Schrodinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network. The second part of the work is devoted to the inverse transformation - the restoration of a signal from a continuous spectrum. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the neural network as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. We show a neural network capable of reconstructing a signal from an already denoised continuous spectrum.
Download poster here