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 3-D visualization in the field of magnetic resonance imaging (MRI). The authors present the optimal transformation for simultaneous segmentation of a desired feature and correction of partial volume averaging effects (CPV), while maximizing of the signal-to-noise ratio of the desired feature. It is proved that CPV requires the removal of the interfering features from the scene. It is also proved that CPV can be achieved merely by a linear transformation. It is finally shown that the optimal transformation matrix is easily obtained using the Gram-Schmidt orthogonalization procedure, which is numerically stable