On the design of filters for fourier and oSVD-based deconvolution in bolus tracking perfusion MRI
On the design of filters for fourier and oSVD-based deconvolution in bolus tracking perfusion MRI
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DOI：
10.1007/s10334-010-0217-8
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发表时间：
2010-06-01
影响因子：
2.3
通讯作者：
Kiselev, Valerij G.
中科院分区：
文献类型：
--
作者：
Gall, Peter;Emerich, Philipp;Kiselev, Valerij G.
团注跟踪血流灌注评估依赖于遵循示踪剂动力学模型的动脉和组织体素中示踪剂浓度时间进程的去卷积。利用傅立叶和循环奇异值分解(OSVD)的数学等价性，提出了一种在傅立叶域设计数据驱动的Tikhonov正则化滤波器的方法，并将其与基于奇异值分解(SVD)的方法进行了比较。利用模拟，作为组织和动脉曲线之间的一阶矩差和输入数据的对比度噪声比(动脉中的CNR(A)和组织中的CNR(T))的函数来确定使统计误差和系统误差之和最小的最佳参数。在仿真和实测数据中对该方法的性能进行了评估，并与oSVD方法进行了比较。与恒定门限的oSVD方法相比，该方法得到了较小的流量低估，特别是在高流量情况下。然而，这种改善是以流量价值不确定性增加为代价的。将Tikhonov正则化参数转换为自适应的oSVD阈值与文献中的结果吻合较好，该方法是一种设计数据驱动的滤波器的综合方法，可以很容易地适应特定的需求。
Bolus tracking perfusion evaluation relies on the deconvolution of a tracers concentration time-courses in an arterial and a tissue voxel following the tracer kinetic model. The object of this work is to propose a method to design a data-driven Tikhonov regularization filter in the Fourier domain and to compare it to the singular value decomposition (SVD)-based approaches using the mathematical equivalence of Fourier and circular SVD (oSVD).The adaptive filter is designed using Tikhonov regularization that depends on only one parameter. Using a simulation, such an optimal parameter that minimizes the sum of statistical and systematic error is determined as a function of the first moment difference between the tissue and the arterial curve and the contrast to noise ratios of the input data (CNR (a) in arteries and CNR (t) in tissue). The performance of the method is evaluated and compared to oSVD in simulations and measured data.The proposed method yields a smaller flow underestimation especially for high flows when compared to the oSVD approach with constant threshold. However, this improvement comes to the price of an increased uncertainty of the flow values. The translation of the Tikhonov regularization parameter to an adaptive oSVD-threshold is in good agreement with the literature.The proposed method is a comprehensive approach for the design of data-driven filters that can be easily adapted to specific needs.