  Sparse representation with respect to an overcomplete dictionary is often
used when regularizing inverse problems in signal and image processing. In
recent years, the Convolutional Sparse Coding (CSC) model, in which the
dictionary consists of shift-invariant filters, has gained renewed interest.
While this model has been successfully used in some image processing problems,
it still falls behind traditional patch-based methods on simple tasks such as
denoising.
  In this work we provide new insights regarding the CSC model and its
capability to represent natural images, and suggest a Bayesian connection
between this model and its patch-based ancestor. Armed with these observations,
we suggest a novel feed-forward network that follows an MMSE approximation
process to the CSC model, using strided convolutions. The performance of this
supervised architecture is shown to be on par with state of the art methods
while using much fewer parameters.
