Parallelizable Bayesian tomography algorithms with rapid,guaranteed convergence
Zheng, J.; Saquib, S.S.; Sauer, K.; Bouman, C.A.
Image Processing, IEEE Transactions on
Volume 9, Issue 10, Oct 2000 Page(s):1745 - 1759
Digital Object Identifier 10.1109/83.869186
Summary:Bayesian tomographic reconstruction algorithms generally require
the efficient optimization of a functional of many variables. In this
setting, as well as in many other optimization tasks, functional
substitution (FS) has been widely applied to simplify each step of the
iterative process. The function to be minimized is replaced locally by
an approximation having a more easily manipulated form, e.g., quadratic,
but which maintains sufficient similarity to descend the true functional
while computing only the substitute. We provide two new applications of
FS methods in iterative coordinate descent for Bayesian tomography. The
first is a modification of our coordinate descent algorithm with
one-dimensional (1-D) Newton-Raphson approximations to an alternative
quadratic which allows convergence to be proven easily. In simulations,
we find essentially no difference in convergence speed between the two
techniques. We also present a new algorithm which exploits the FS method
to allow parallel updates of arbitrary sets of pixels using computations
similar to iterative coordinate descent. The theoretical potential speed
up of parallel implementations is nearly linear with the number of
processors if communication costs are neglected
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