Monotonic algorithms for transmission tomography
Monotonic algorithms for transmission tomography
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DOI：
10.1109/42.802758
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发表时间：
1999-09-01
影响因子：
10.6
通讯作者：
Fessler, JA
中科院分区：
文献类型：
--
作者：
Erdogan, H;Fessler, JA
我们提出了一个框架，设计快速和单调算法的透射断层扫描惩罚似然图像重建。新算法基于对数似然的抛物面代理函数，由于对数似然函数的形式，可以找到保证单调性的低曲率代理函数。与以前的方法不同，所提出的代理函数导致单调算法，即使是非凸的日志可能性，由于背景事件，如分散和随机巧合。每一次迭代只计算一次似然项的梯度和曲率。由于该问题在每次迭代时都得到简化，因此与直接极小化目标的现有算法相比，其CPU时间更少，但收敛速度相当。新算法的简单性、单调性和快速性是相当有吸引力的。使用真实的和模拟PET透射扫描的算法的收敛速度证明。
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 form 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. The convergence rates of the algorithms are demonstrated using real and simulated PET transmission scans.