  Deep learning models are state-of-the-art in compressive spectral imaging
(CSI) recovery. These methods use a deep neural network (DNN) as an image
generator to learn non-linear mapping from compressed measurements to the
spectral image. For instance, the deep spectral prior approach uses a
convolutional autoencoder network (CAE) in the optimization algorithm to
recover the spectral image by using a non-linear representation. However, the
CAE training is detached from the recovery problem, which does not guarantee
optimal representation of the spectral images for the CSI problem. This work
proposes a joint non-linear representation and recovery network (JR2net),
linking the representation and recovery task into a single optimization
problem. JR2net consists of an optimization-inspired network following an ADMM
formulation that learns a non-linear low-dimensional representation and
simultaneously performs the spectral image recovery, trained via the end-to-end
approach. Experimental results show the superiority of the proposed method with
improvements up to 2.57 dB in PSNR and performance around 2000 times faster
than state-of-the-art methods.
