Reconstruction of Dynamic PET Data Using Spatio-Temporal Wavelet l1 Regularization

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. proposed an l1 regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets that are specially tailored to model time activity curves (TACs) in PET. We show the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarie wavelets for a 1-D TAC fitting experiment and a tomographic reconstruction experiment.