  In this paper, the traditional model based variational method and learning
based algorithms are naturally integrated to address mixed noise removal
problem. To be different from single type noise (e.g. Gaussian) removal, it is
a challenge problem to accurately discriminate noise types and levels for each
pixel. We propose a variational method to iteratively estimate the noise
parameters, and then the algorithm can automatically classify the noise
according to the different statistical parameters. The proposed variational
problem can be separated into regularization, synthesis, parameter estimation
and noise classification four steps with the operator splitting scheme. Each
step is related to an optimization subproblem. To enforce the regularization,
the deep learning method is employed to learn the natural images priori.
Compared with some model based regularizations, the CNN regularizer can
significantly improve the quality of the restored images. Compared with some
learning based methods, the synthesis step can produce better reconstructions
by analyzing the recognized noise types and levels. In our method, the
convolution neutral network (CNN) can be regarded as an operator which
associated to a variational functional. From this viewpoint, the proposed
method can be extended to many image reconstruction and inverse problems.
Numerical experiments in the paper show that our method can achieve some
state-of-the-art results for mixed noise removal.
