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- First define your problem: if are the two gel
images, written as
functions on the plane, then they are related by
(1) *residual*error is the difference between the `aligned gels'. - So all we have to do is estimate and split into two
components: interesting stuff and artefacts:
(2) - Easy? Well...it's just a tad ill-posed, like all the interesting problems
in image analysis. After all, we could set , the identity, then
would just be the difference between the raw images - or we could
set to be a constant translation to be added to every point
in the image, ie
(3) - In other words, we must use
*prior*knowledge to solve this one. And about the only thing we can be sure about is that the is a*smooth*function of . - Ideally, we would like a
*Maximum a Posteriori*(MAP) estimate of , along the lines of(4) *E*denotes expectation and the sample mean of .

5/31/2000