Camouflaged Deconvolution With Application to Blood Curve Modeling in FDG PET Studies

Abstract

Abstract Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the degree of smoothness of the solution. We use simulation studies matched to the application to evaluate statistical performance. These simulations find that the convergence of the regularization estimator is largely unaffected by the lack of information about the convolution kernels. We illustrate the methodology by application to a blood curve modeling problem arising in the context of positron emission tomography (PET) studies with flurodeoxyglucose (FDG), a commonly used glucose tracer. The results show promise towards the goal of obtaining reliable metabolic information with much more limited blood sampling.