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Dynamic PET reconstruction using wavelet regularization with adapted basis functions

Verhaeghe, Jeroen
D'Asseler, Yves
Lemahieu, Ignace
Unser, Michael
Published in IEEE Transactions on Medical Imaging. 2008, vol. 27, no. 7, p. 943-959
Abstract Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an l(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 usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-LemariE wavelets in a series of experiments: the 1-D fitting of TACs, and the tomographic reconstruction of both simulated and clinical 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.
Keywords AlgorithmsArtificial IntelligenceCluster AnalysisComputer SimulationData Interpretation, StatisticalFeedbackFourier AnalysisHumansImaging, Three-Dimensional/*methodsInformation Storage and Retrieval/methodsKidney/radionuclide imagingLiver/radionuclide imagingPattern Recognition, AutomatedPositron-Emission Tomography/*methods*Signal Processing, Computer-AssistedTime Factors
PMID: 18599400
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Research group Traitement d'images médicales (893)
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VERHAEGHE, Jeroen et al. Dynamic PET reconstruction using wavelet regularization with adapted basis functions. In: IEEE Transactions on Medical Imaging, 2008, vol. 27, n° 7, p. 943-959. https://archive-ouverte.unige.ch/unige:19114

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Deposited on : 2012-03-27

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