## EECS CSPL SEMINAR SERIES

WINTER TERM 1998

Hakan Erdogan
#

### erdogan@eecs.umich.edu

###

### Department of Electrical Engineering and Computer
Science

### University of Michigan

Thursday, March 19, 1998

4:30-5:30 pm

1001 EECS

### "Accelerated Monotonic Algorithms for Transmission
Tomography

abstract-

We present a framework for designing fast and monotonic algorithms
for
transmission tomography penalized-likelihood image
reconstruction. The
new algorithms are based on paraboloidal surrogate
functions for the
log-likelihood. Due to the shape of the log-likelihood
function, it
is possible to find low curvature surrogate functions that
guarantee
monotonicity. Unlike previous methods, the proposed
surrogate
functions lead to monotonic algorithms even for the
nonconvex log-likelihood
that arises due to background events such as
scatter and
random coincidences. The gradient and the curvature of the
likelihood
terms are evaluated only once per iteration. Since the
problem is
simplified at each iteration, the CPU time is less
than that of
current algorithms which directly minimize the
objective, yet the
convergence rate is comparable. The simplicity,
monotonicity and
speed of the new algorithms are quite attractive. It is
easy to get
parallelizable algorithms by applying previously introduced
``grouped
coordinate'' ideas to the simple quadratic surrogate
function. The
performance of the algorithms is demonstrated on real and
simulated
PET transmission scans.

Biosketch -

Please refer to the homepage
found through the link shown above.

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