Single Photon Emission Computed Tomography Example

Single photon emission computed tomography (SPECT) is a medical imaging technology. The patient is treated with a radioactive substance that releases individual gamma rays (in small amounts, so as to be detectable but not damaging to the patient). Some of these gamma rays are detected by a special camera, and then a classic inverse problem results from the need to infer the original image in the patient from the counts of detected gamma rays. Computer code links hypothesized images to predicted gamma ray counts. The primary goal is to reconstruct the features of the underlying object, such as a patient’s brain. This image is typically desired at a particular resolution, and only one type of data is collected, so there is nothing inherently multiscale here. However, a fully Bayesian analysis requires the use of Markov chain Monte Carlo methods, and the chain can take a long time to run because of poor mixing. The use of multiscale techniques can greatly speed up the computational aspects of the problem, improving the statistical inference that can be done in a reasonable amount of time. Thus, we demonstrate the implicit methods of Part IV with this example.