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.
