  We present a novel method to reconstruct a spectral central view and its
aligned disparity map from spatio-spectrally coded light fields. Since we do
not reconstruct an intermediate full light field from the coded measurement, we
refer to this as principal reconstruction. The coded light fields correspond to
those captured by a light field camera in the unfocused design with a
spectrally coded microlens array. In this application, the spectrally coded
light field camera can be interpreted as a single-shot spectral depth camera.
  We investigate several multi-task deep learning methods and propose a new
auxiliary loss-based training strategy to enhance the reconstruction
performance. The results are evaluated using a synthetic as well as a new
real-world spectral light field dataset that we captured using a custom-built
camera. The results are compared to state-of-the art compressed sensing
reconstruction and disparity estimation.
  We achieve a high reconstruction quality for both synthetic and real-world
coded light fields. The disparity estimation quality is on par with or even
outperforms state-of-the-art disparity estimation from uncoded RGB light
fields.
