geoffwoollard
commented
2 years ago See eq 8.21 in https://repository.upenn.edu/cgi/viewcontent.cgi?article=1665&context=physics_papers
While this is derived in the case of 2D alignment, it is applicable to 2D -> 3D reconstruction.
- Ui is the sum over 3D rotations (sum of Bayes "gamma" factors of particle_i to the library of 3D slices)
- Ki is jus the max of the log of the Bayes "gamma" factors
- i is the sum over particles
Thus L can be tracked for each particle: L = sum_i l_i. And over each iteration.
EM guarantees that L goes down each iteration.
TODO: look into tracking l_i, per particle update, not just L over the whole iteration.
p(volume|data) is optimized in the MLE/MAP setting.
Ideally there is a loss that can be computed and tracked as the procedure progresses by iteration.
Perhaps it's related to the residual of empirical noise to assumed model (e.g. white) noise?
TODO: derive how to compute this.