Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime
This work addresses the challenge of solving wave-based inverse problems, particularly in super-resolution regimes, for applications in imaging and scattering analysis, though it appears incremental as it builds on existing deep learning methods with specific architectural and training innovations.
The authors tackled the inverse wave scattering problem across all length scales, including the super-resolution regime, by proposing an end-to-end deep learning framework with a wide-band butterfly network and dynamic noise injection during training. Their framework achieved competitive results in classical regimes and succeeded in super-resolution tasks, such as reconstructing sub-wavelength features and imaging scatterers separated by less than the diffraction limit, while being robust to noise and faster than optimization-based methods.
We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple training procedure that dynamically injects noise during training. While our trained network provides competitive results in classical imaging regimes, most notably it also succeeds in the super-resolution regime where other comparable methods fail. This encompasses both (i) reconstruction of scatterers with sub-wavelength geometric features, and (ii) accurate imaging when two or more scatterers are separated by less than the classical diffraction limit. We demonstrate these properties are retained even in the presence of strong noise and extend to scatterers not previously seen in the training set. In addition, our network is straightforward to train requiring no restarts and has an online runtime that is an order of magnitude faster than optimization-based algorithms. We perform experiments with a variety of wave scattering mediums and we demonstrate that our proposed framework outperforms both classical inversion and competing network architectures that specialize in oscillatory wave scattering data.