Another Bias Correction Method John Ashburner

E = -log{P(y|)} = -i log{k k k(yi)}

In fact, k(yi) does not need to be a Gaussian density. It could be a B-spline with local support. In the limiting case of zeroeth and first degree B-splines, maximising this cost function is equivalent to generating a simple histogram of the data. E has a simple relationship with the entropy.

The bias correction model will also fit within this framework:

E = -log{P(y|,)} = -i log{i() k k k(i()yi)}

B-spline Density Representations

• The algorithm is iterative, and involves alternating between:

• Re-estimating , while holding  fixed.
• Re-estimating , while holding  fixed.

• Re-estimating  involves building a probability density representation of the data, which have been corrected with the current bias estimate.

• Simplest case involves generating a simple histogram.
• An iterative method is needed for B-splines of degree greater than 1.
• Similar to algorithm for ML-EM reconstruction of PET images.
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