Verhaeghe Jeroen, Van de Ville Dimitri, Khalidov Ildar, D'Asseler Yves, Lemahieu Ignace, Unser Michael
Department of Electronics and Information Systems, MEDISIP, Ghent University-IBBT-IBiTech, De Pintelaan 185 block B, B-9000 Ghent, Belgium.
IEEE Trans Med Imaging. 2008;27(7):943-59. doi: 10.1109/TMI.2008.923698.
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.
基于正电子发射断层扫描（PET）数据的断层重建是一个需要正则化的不适定问题。一种有吸引力的方法是施加l(1)正则化约束，这有利于在小波域中得到稀疏解。由于Daubechies等人在2004年开发的迭代算法，这一点可以非常有效地实现。在本文中，我们应用了这项技术并将其扩展用于动态（时空）PET数据的重建。此外，在时间维度上，我们引入了指数样条小波（E - 样条小波），而不是使用经典小波，这种小波是专门为模拟PET中的时间 - 活度曲线（TAC）而设计的。我们表明指数样条小波自然地源于示踪剂分布动力学的房室描述。我们解决了“最优”E - 样条参数（极点和零点）的选择问题，并研究了它们对重建质量的影响。在一系列实验中，我们证明了时空正则化的有用性以及E - 样条小波相对于传统的Battle - LemariE小波的优越性能：TAC的一维拟合以及模拟和临床数据的断层重建。我们发现，在重建的信噪比（SNR）和小波系数的稀疏性方面，E - 样条小波优于传统小波。基于我们的模拟，我们得出结论，用E - 样条小波代替传统小波可在检测到的符合事件减少40%的情况下实现相同的重建质量，这意味着在相同计数数量下图像质量得到改善，或者在相同图像质量下患者的辐射暴露减少。
