Wednesday, June 6, 2012

I'm stuck, so going to try to redefine (simplify) the problem itself

Hmm my problem is motion compensation, in Computed Tomography (CT) (as in 'CT or CAT scans').

The usual tomographic reconstruction technique assumes that the body, or object, is stationary.
$f(x)$

Now _my_ object is dynamic (think lung motion for example):
$f (x, t)$

So to scan and reconstruct a dynamic object like a breathing lung is the problem I chose to work on.

And after several attempts at it, I think I am going to simplify the problem itself, because currently I assume total generality of both original object and the motion, making no assumptions about either of them.
Several solutions exist because the problem is not invertible uniquely, because of the nature of the whole thing.
So I try to obtain one solution (among several solutions that exist) by minimizing some objective.

And i'm stuck. At least, the whole thing I have right now, looks inelegant and clumsy that I don't find any thrill of  continuing it this way. (In other words i ended up with some nasty nonlinear PDEs.)

And since I've been stuck for a while I am now going to simplify the problem itself, and then solve the simpler problem.

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