Joint Reconstruction and Calibration using Regularization by Denoising
This work is significant for researchers and practitioners in inverse problems, particularly in medical imaging and other fields where measurement operator uncertainties are common, by extending a powerful reconstruction framework to more realistic scenarios.
This paper addresses the limitation of Regularization by Denoising (RED) methods, which typically require precise knowledge of the measurement operator, by introducing Calibrated RED (Cal-RED). Cal-RED enables simultaneous calibration of the measurement operator and reconstruction of the image, demonstrated effectively in computerized tomography (CT) with perturbed projection angles.
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.