  Modern digital cameras rely on the sequential execution of separate image
processing steps to produce realistic images. The first two steps are usually
related to denoising and demosaicking where the former aims to reduce noise
from the sensor and the latter converts a series of light intensity readings to
color images. Modern approaches try to jointly solve these problems, i.e. joint
denoising-demosaicking which is an inherently ill-posed problem given that
two-thirds of the intensity information is missing and the rest are perturbed
by noise. While there are several machine learning systems that have been
recently introduced to solve this problem, the majority of them relies on
generic network architectures which do not explicitly take into account the
physical image model. In this work we propose a novel algorithm which is
inspired by powerful classical image regularization methods, large-scale
optimization, and deep learning techniques. Consequently, our derived iterative
optimization algorithm, which involves a trainable denoising network, has a
transparent and clear interpretation compared to other black-box data driven
approaches. Our extensive experimentation line demonstrates that our proposed
method outperforms any previous approaches for both noisy and noise-free data
across many different datasets. This improvement in reconstruction quality is
attributed to the rigorous derivation of an iterative solution and the
principled way we design our denoising network architecture, which as a result
requires fewer trainable parameters than the current state-of-the-art solution
and furthermore can be efficiently trained by using a significantly smaller
number of training data than existing deep demosaicking networks. Code and
results can be found at https://github.com/cig-skoltech/deep_demosaick
