An approximate bootstrap technique for variance estimation in parametric images

Parametric imaging procedures offer the possibility of comprehensive assessment of tissue metabolic activity. Estimating variances of these images is important for the development of inference tools in a diagnostic setting. However, these are not readily obtained because the complexity of the radio-tracer models used in the generation of a parametric image makes analytic variance expressions intractable. On the other hand, a natural extension of the usual bootstrap resampling approach is infeasible because of the expanded computational effort. This paper suggests a computationally practical, approximate simulation strategy to variance estimation. Results of experiments done to evaluate the approach in a simplified model one-dimensional problem are very encouraging. Diagnostic checks performed on a single real-life positron emission tomography (PET) image to test for the feasibility of applying the procedure in a real-world PET setting also show some promise. The suggested methodology is evaluated here in the context of parametric images extracted by mixture analysis; however, the approach is general enough to extend to other parametric imaging methods.