Correction of bias field in MR images using singularity function analysis

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR image's low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.