Dynamic PET Reconstruction Using Wavelet Regularization With Adapted Basis Functions

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an 1-regularization constraint, which favors sparse solutions in the wavelet domain. This can be achieved quite efficiently thanks to the iterative algorithm developed by Daubechies et al., 2004. In this paper, we apply this technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data. Moreover, instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET. We show that the exponential-spline wavelets naturally arise from the compartmental description of the dynamics of the tracer distribution. We address the issue of the selection of the "optimal" E-spline parameters (poles and zeros) and we investigate their effect on reconstruction quality. We demonstrate the...

• Type: Journal
• Year: 2008
• Where: TMI
• Authors: J. Verhaeghe, Dimitri Van De Ville, I. Khalidov, Yves D'Asseler, Ignace Lemahieu, Michael Unser
• Keywords: Conventional Wavelets, TMI 2008, Tomographic Reconstruction, Wavelets