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.