Image recovery using iterative data refinement with relaxation

Abstract

Iterative data refinement (IDR) is a general procedure for estimating data that would have been collected by an ideal measuring device from data that were collected by an actual measuring device. We show that IDR is general enough to encompass such well-accepted image recovery methods as the Gerchberg-Saxton algorithm and the error reduction and hybrid input-output methods of Fienup. The generalizations provided by IDR give new insights into the nature of such algorithms and, in particular, allow us to introduce the notion of relaxation into them. Along similar lines, DR provides a common framework within which new algorithms can be developed for improved magnetic resonance imaging (MRI). We apply the approach of IDR to a specific problem in MRI, namely, to the correction of spatially dependent blurs due to transverse relaxation. The algorithm is designed to reconstruct 12-weighted spin density images with improved spatial resolution. The practical computational significance of using the IDR approach is illustrated by the reconstruction of mathematical phantoms. We find that overrelaxation of the algorithm can improve computational speed by up to a factor of five.