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Reconstruction of dynamic PET data using spatio-temporal wavelet l(1) regularization

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Abstract
Tomographic reconstruction from PET data is an W-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l(1) 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.
Keywords
CARDINAL EXPONENTIAL SPLINES, ALGORITHM

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Chicago
Verhaeghe, Jeroen, Dimitri Van De Ville, Ildar Khalidov, Michael Unser, YVES D’ASSELER, and Ignace Lemahieu. 2007. “Reconstruction of Dynamic PET Data Using Spatio-temporal Wavelet L(1) Regularization.” In 2007 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-16, 6540–6543. New York: IEEE.
APA
Verhaeghe, Jeroen, Van De Ville, D., Khalidov, I., Unser, M., D’ASSELER, Y., & Lemahieu, I. (2007). Reconstruction of dynamic PET data using spatio-temporal wavelet l(1) regularization. 2007 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-16 (pp. 6540–6543). Presented at the 29th Annual International Conference of the IEEE-Engineering-in-Medicine-and-Biology-Society, New York: IEEE.
Vancouver
1.
Verhaeghe J, Van De Ville D, Khalidov I, Unser M, D’ASSELER Y, Lemahieu I. Reconstruction of dynamic PET data using spatio-temporal wavelet l(1) regularization. 2007 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-16. New York: IEEE; 2007. p. 6540–3.
MLA
Verhaeghe, Jeroen, Dimitri Van De Ville, Ildar Khalidov, et al. “Reconstruction of Dynamic PET Data Using Spatio-temporal Wavelet L(1) Regularization.” 2007 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-16. New York: IEEE, 2007. 6540–6543. Print.
@inproceedings{750575,
  abstract     = {Tomographic reconstruction from PET data is an W-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l(1) 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.},
  author       = {Verhaeghe, Jeroen and Van De Ville, Dimitri and Khalidov, Ildar and Unser, Michael and D'Asseler, Yves and Lemahieu, Ignace},
  booktitle    = {2007 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-16},
  isbn         = {978-1-4244-0787-3},
  issn         = {1094-687X},
  language     = {eng},
  location     = {Lyon, FRANCE},
  pages        = {6540--6543},
  publisher    = {IEEE},
  title        = {Reconstruction of dynamic PET data using spatio-temporal wavelet l(1) regularization},
  url          = {http://dx.doi.org/10.1109/IEMBS.2007.4353858},
  year         = {2007},
}

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