  We demonstrate the use of deep learning for fast spectral deconstruction of
speckle patterns. The artificial neural network can be effectively trained
using numerically constructed multispectral datasets taken from a measured
spectral transmission matrix. Optimized neural networks trained on these
datasets achieve reliable reconstruction of both discrete and continuous
spectra from a monochromatic camera image. Deep learning is compared to
analytical inversion methods as well as to a compressive sensing algorithm and
shows favourable characteristics both in the oversampling and in the sparse
undersampling (compressive) regimes. The deep learning approach offers
significant advantages in robustness to drift or noise and in reconstruction
speed. In a proof-of-principle demonstrator we achieve real time recovery of
hyperspectral information using a multi-core, multi-mode fiber array as a
random scattering medium.
