We propose a convolutional recurrent sparse auto-encoder
model. The model consists of a sparse encoder, which is a
convolutional extension of the learned ISTA (LISTA) method,
and a linear convolutional decoder. Our strategy offers a simple
method for learning a task-driven sparse convolutional
dictionary (CD), and producing an approximate convolutional
sparse code (CSC) over the learned dictionary. We trained
the model to minimize reconstruction loss via gradient decent
with back-propagation and have achieved competitve
results to KSVD image denoising and to leading CSC methods
in image inpainting requiring only a small fraction of
their run-time.