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

## J. Verhaeghe, D. Van De Ville, I. Khalidov, M. Unser, Y. D'Asseler, I. Lemahieu

### Proceedings of the Twenty-Ninth Annual International Conference of the IEEE Engineering in Medicine and Biology Society, in conjunction with the biennial Conference of the French Society of Biological and Medical Engineering (EMBC'07), Lyon, French Republic, August 23-26, 2007, pp. 6539-6542.

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. [1] 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-Lemarié wavelets for a 1-D TAC fitting experiment and a tomographic reconstruction experiment.

### References

1. I. Daubechies, M. Defrise, C. De Mol, "An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint," Communications on Pure and Applied Mathematics, vol. 57, no. 11, pp. 1413-1457, November 2004.

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AUTHOR="Verhaeghe, J. and Van De Ville, D. and Khalidov, I. and Unser,
M. and D'Asseler, Y. and Lemahieu, I.",
TITLE="Reconstruction of Dynamic {PET} Data Using Spatio-Temporal
Wavelet $\ell_{1}$ Regularization",
BOOKTITLE="Proceedings of the Twenty-Ninth Annual International
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