Many Heads Are Better Than One: Jointly Removing Bias from Multiple MRIs Using Nonparametric Maximum Likelihood

The correction of multiplicative bias in magnetic resonance images is an important problem in medical image processing, especially as a preprocessing step for quantitative measurements and other numerical procedures. Most previous approaches have used a maximum likelihood method to increase the probability of the pixels in a single image by adaptively estimating a correction to the unknown image bias field. The pixel probabilities are defined either in terms of a pre-existing tissue model, or nonparametrically in terms of the image's own pixel values. In both cases, the specific location of a pixel in the image does not influence the probability calculation. Our approach, similar to methods of joint registration, simultaneously eliminates the bias from a set of images of the same anatomy, but from different patients. We use the statistics from the same location across different patients' images, rather than within an image, to eliminate bias fields from all of the images simultaneously. Evaluating the likelihood of a particular voxel in one patient's scan with respect to voxels in the same location in a set of other patients' scans disambiguates effects that might be due to either bias fields or anatomy. We present a variety of "two-dimensional" experimental results (working with one image from each patient) showing how our method overcomes serious problems experienced by other methods. We also present preliminary results on full three-dimensional volume correction across patients.