Eigenimage filtering in MR imaging

This article presents the technical aspects of a linear filter, referred to as eigenimage filtering, and its applications in magnetic resonance (MR) imaging. The technique is used to obtain a single composite image depicting a particular feature of interest while suppressing one or more interfering features. The appropriate weighting components to be used in the linear filter are determined on the criterion that the desired feature is enhanced while the interfering features are suppressed. The criterion is expressed mathematically as a ratio. By applying Rayleigh's principle, the ratio is maximized by finding the eigenvector associated with the maximum eigenvalue of the corresponding generalized eigenvalue problem. The appropriate weighting factors for the linear filter are the elements of the eigenvector which maximize the ratio. The utilization of the technique is demonstrated in its application to a simulated MR image sequence as well as to acquired MR image sequences of a normal and an abnormal brain.