  We solve the analysis sparse coding problem considering a combination of
convex and non-convex sparsity promoting penalties. The multi-penalty
formulation results in an iterative algorithm involving proximal-averaging. We
then unfold the iterative algorithm into a trainable network that facilitates
learning the sparsity prior. We also consider quantization of the network
weights. Quantization makes neural networks efficient both in terms of memory
and computation during inference, and also renders them compatible for
low-precision hardware deployment. Our learning algorithm is based on a variant
of the ADAM optimizer in which the quantizer is part of the forward pass and
the gradients of the loss function are evaluated corresponding to the quantized
weights while doing a book-keeping of the high-precision weights. We
demonstrate applications to compressed image recovery and magnetic resonance
image reconstruction. The proposed approach offers superior reconstruction
accuracy and quality than state-of-the-art unfolding techniques and the
performance degradation is minimal even when the weights are subjected to
extreme quantization.
