Thursday, March 19, 1998
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.
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