Optimal transformation for correcting partial volume averaging effects in magnetic resonance imaging

Segmentation of a feature of interest while correcting for partial volume averaging effects is a major tool for identification of hidden abnormalities, fast and accurate volume calculation, and three-dimensional visualization in the field of magnetic resonance imaging (MRI). The authors discuss the optimal transformation for simultaneous segmentation of a desired feature and correction of partial volume averaging effects while maximizing the signal-to-noise ratio (SNR) of the desired feature. It is proved that correction of partial volume averaging effects requires the removal of the interfering features from the scene. It is also proved that correction of partial volume averaging effects can be achieved merely by a linear transformation. It is shown that the optimal transformation matrix is easily obtained using the Gram-Schmidt orthogonalization procedure which is numerically stable. Applications of the technique to MRI simulation, phantom, and brain images are shown. It is shown that in all cases the desired feature is segmented from the interfering features and partial volume information is visualized in the resulting transformed images