Statistical estimation with Kronecker products in positron emission tomography

A method for linear statistical analysis of multidimensional imaging data is presented. It is applicable for a class of design and covariance matrices which involve Kronecker products. An efficient algorithm which allows for application of the method to large multidimensional data volumes is given. This has direct application to neuroimaging, and here the technique is applied to positron emission tomography (PET) data. PET is an in vivo functional imaging technique that measures biological processes such as blood flow and receptor concentrations. Here, the algorithm is used to correct for resolution degradation in these images. This process is typically referred to as PET partial volume correction. Examples involving both measured phantom and human data are given. This rapid algorithm leads to advances in the types of quantitative brain imaging studies that can be performed.