Recent interest in hypothesis testing on functional imaging data has spurred the development of several statistical techniques. The purpose of this paper is to provide a method to reduce the computational intensity associated with randomization tests of positron emission tomography imaging data. We discuss the advantages and disadvantages of traditional distributional hypothesis testing versus the advantages and disadvantages of randomization tests. A method for reducing the computational intensity of randomization uses a conjunction of updating and sequenching and results in significantly reduced processing. The running times of randomization methods are compared.