  Modeling statistical regularity plays an essential role in ill-posed image
processing problems. Recently, deep learning based methods have been presented
to implicitly learn statistical representation of pixel distributions in
natural images and leverage it as a constraint to facilitate subsequent tasks,
such as color constancy and image dehazing. However, the existing CNN
architecture is prone to variability and diversity of pixel intensity within
and between local regions, which may result in inaccurate statistical
representation. To address this problem, this paper presents a novel fully
point-wise CNN architecture for modeling statistical regularities in natural
images. Specifically, we propose to randomly shuffle the pixels in the origin
images and leverage the shuffled image as input to make CNN more concerned with
the statistical properties. Moreover, since the pixels in the shuffled image
are independent identically distributed, we can replace all the large
convolution kernels in CNN with point-wise ($1*1$) convolution kernels while
maintaining the representation ability. Experimental results on two
applications: color constancy and image dehazing, demonstrate the superiority
of our proposed network over the existing architectures, i.e., using
1/10$\sim$1/100 network parameters and computational cost while achieving
comparable performance.
