MRI at high magnetic fields (> 3.0 T) is complicated by strong inhomogeneous radio-frequency fields, sometimes
termed the "bias field". These lead to nonuniformity of image intensity, greatly complicating further analysis
such as registration and segmentation. Existing methods for bias field correction are effective for 1.5 T or
3.0 T MRI, but are not completely satisfactory for higher field data. This paper develops an effective bias field
correction for high field MRI based on the assumption that the nonuniformity is smoothly varying in space. Also,
nonuniformity is quantified and unmixed using high order neighborhood statistics of intensity cooccurrences.
They are computed within spherical windows of limited size over the entire image. The restoration is iterative
and makes use of a novel stable stopping criterion that depends on the scaled entropy of the cooccurrence
statistics, which is a non monotonic function of the iterations; the Shannon entropy of the cooccurrence statistics
normalized to the effective dynamic range of the image. The algorithm restores whole head data, is robust to
intense nonuniformities present in high field acquisitions, and is robust to variations in anatomy. This algorithm
significantly improves bias field correction in comparison to N3 on phantom 1.5 T head data and high field 4 T
human head data.
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