  Regularization by denoising (RED) is a broadly applicable framework for
solving inverse problems by using priors specified as denoisers. While RED has
been shown to provide state-of-the-art performance in a number of applications,
existing RED algorithms require exact knowledge of the measurement operator
characterizing the imaging system, limiting their applicability in problems
where the measurement operator has parametric uncertainties. We propose a new
method, called Calibrated RED (Cal-RED), that enables joint calibration of the
measurement operator along with reconstruction of the unknown image. Cal-RED
extends the traditional RED methodology to imaging problems that require the
calibration of the measurement operator. We validate Cal-RED on the problem of
image reconstruction in computerized tomography (CT) under perturbed projection
angles. Our results corroborate the effectiveness of Cal-RED for joint
calibration and reconstruction using pre-trained deep denoisers as image
priors.
