|Spatio-Temporal Reconstruction of PET Data Using Wavelet Regularization|
Investigators: Jeroen Verhaeghe, Ildar Khalidov, Dimitri Van De Ville, Michael Unser
Summary: We reconstruct dynamic (spatio-temporal) PET data using regularization based on exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET.
Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an ℓ1 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.
|Spatio-temporal reconstruction of the NCAT phantom. Left: Filtered back-projection, Middle: Wavelet-based temporal regularization, Right: Wavelet-based spatio-temporal regularization.|
In this work, we apply the iterated-thresholding technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data.
We find that the E-spline wavelets outperform the conventional wavelets in terms of the reconstructed signal-to-noise ratio (SNR) and the sparsity of the wavelet coefficients. Based on our simulations, we conclude that replacing the conventional wavelets with E-spline wavelets leads to equal reconstruction quality for a 40% reduction of detected coincidences, meaning an improved image quality for the same number of counts or, equivalently, a reduced exposure to the patient for the same image quality.
- 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 usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarié wavelets in a series of experiments.
Collaborations: Dr. Jeroen Verhaeghe (MNI), Prof. Michael Unser
J. Verhaeghe, D. Van De Ville, I. Khalidov, Y. D'Asseler, I. Lemahieu, M. Unser, "Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions," IEEE Transactions on Medical Imaging, vol. 27, no. 7, pp. 943-959, July 2008.