Accelerated monotonic algorithms for transmission tomography

We present a framework for designing fast and mono-tonic algorithms for transmission tomography penalized-likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log-likelihood. Due to the form of the log-likelihood func-tion, it is possible to find low curvature surrogate func-tions that guarantee monotonicity. Unlike previous meth-ods, the proposed surrogate functions lead to monotonic al-gorithms even for the nonconvex log- likelihood that arises due to background events such as scatter and random coin-cidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the prob-lem is simplified, the CPU time per iteration is less than that of current algorithms which directly minimize the ob-jective, yet the convergence rate is comparable. The sim-plicity, monotonicity and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real PET transmission scans.