  Image domain prior models have been shown to improve the quality of
reconstructed images, especially when data are limited. Pre-processing of raw
data, through the implicit or explicit inclusion of data domain priors have
separately also shown utility in improving reconstructions. In this work, a
principled approach is presented allowing the unified integration of both data
and image domain priors for improved image reconstruction. The consensus
equilibrium framework is extended to integrate physical sensor models, data
models, and image models. In order to achieve this integration, the
conventional image variables used in consensus equilibrium are augmented with
variables representing data domain quantities. The overall result produces
combined estimates of both the data and the reconstructed image that is
consistent with the physical models and prior models being utilized. The prior
models used in both domains in this work are created using deep neural
networks. The superior quality allowed by incorporating both data and image
domain prior models is demonstrated for two applications: limited-angle CT and
accelerated MRI. The prior data model in both these applications is focused on
recovering missing data. Experimental results are presented for a 90 degree
limited-angle tomography problem from a real checked-bagged CT dataset and a 4x
accelerated MRI problem on a simulated dataset. The new framework is very
flexible and can be easily applied to other computational imaging problems with
imperfect data.
