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.