Rank-shaping regularization of exponential spectral analysis for application to functional parametric mapping
Rank-shaping regularization of exponential spectral analysis for application to functional parametric mapping
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DOI：
10.1088/0031-9155/48/23/002
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发表时间：
2003-12-07
影响因子：
3.5
通讯作者：
Cunningham, VJ
中科院分区：
文献类型：
--
作者：
Turkheimer, FE;Hinz, R;Cunningham, VJ
区室模型被广泛用于正电子发射断层扫描（PET）获得的动力学研究的数学建模。数值问题涉及到衰减实指数与输入函数卷积的和的估计。在指数谱分析（SA）中，指数函数的非线性估计被一组预定义的指数基函数的系数的线性估计所取代。这种设置保证了快速估计和实现全局最优。然而，由于对噪声的高灵敏度，并且由于算法中实现的正性约束，SA不能扩展到参考区域建模。在本文中，通过定义适当正则化的新的秩形（RS）估计量来解决SA的限制。通过指数基的奇异值分解得到无约束的最小二乘解。收缩参数取决于预期的信噪比。通过对模拟和真实数据集的应用，表明在PET研究产生功能参数图的情况下，RS改进和扩展了SA性质。
Compartmental models are widely used for the mathematical modelling of dynamic studies acquired with positron emission tomography (PET). The numerical problem involves the estimation of a sum of decaying real exponentials convolved with an input function. In exponential spectral analysis (SA), the nonlinear estimation of the exponential functions is replaced by the linear estimation of the coefficients of a predefined set of exponential basis functions. This set-up guarantees fast estimation and attainment of the global optimum. SA, however, is hampered by high sensitivity to noise and, because of the positivity constraints implemented in the algorithm, cannot be extended to reference region modelling. In this paper, SA limitations are addressed by a new rank-shaping (RS) estimator that defines an appropriate regularization. over an unconstrained least-squares solution obtained through singular value decomposition of the exponential base. Shrinkage parameters are conditioned on the expected signal-to-noise ratio. Through application to simulated and real datasets, it is shown that RS ameliorates and extends SA properties in the case of the production of functional parametric maps from PET studies.