SIAM Journal on Imaging Sciences, Volume 14, Issue 1, Page 418-439, January 2021.
Parametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. Classical approaches to parametric imaging rely on linearized schemes that, on the one hand, are computationally effective but, on the other hand, provide information just on a very limited number of parameters (typically two). Possible nonlinearized approaches require the pixelwise numerical solution of compartmental nonlinear ill-posed inverse problems and therefore typically imply a notable computational burden. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling trust-region method. The main advantages of this approach are both that it is a regularization method (and therefore it reduces the numerical instabilities in the reconstructed images) and that it is significantly faster than other algorithms in the optimization market (and therefore it may be utilized for clinical applications). The validation of this approach is realized in a simulation framework for brain imaging and also in the case of an experimental set of nuclear medicine data acquired from a murine model. Comparison of performances is made with respect to a regularized Gauss--Newton scheme and a standard nonlinear bound-constrained least-squares algorithm.

中文翻译：

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动态PET数据参数化成像的正规化仿射缩放比例信任区域方法

SIAM影像科学杂志，第14卷，第1期，第418-439页，2021年1月。
核医学数据的参数成像利用动态功能图像来重建与注入生物组织中的特定示踪剂的代谢有关的动力学参数图。参数成像的经典方法依赖于线性化方案，该方案一方面在计算上有效，但另一方面仅在数量非常有限的参数（通常为两个）上提供信息。可能的非线性化方法需要隔室非线性不适定逆问题的像素级数值解，因此通常意味着显着的计算负担。在本文中，我们介绍了一种基于标准仿射缩放比例信赖域方法的正规化版本的参数成像快速数值优化方案。这种方法的主要优点是它既是一种正则化方法（因此减少了重建图像中的数值不稳定性），又比优化市场中的其他算法快得多（因此可以用于临床应用） ）。这种方法的验证是在用于大脑成像的模拟框架中实现的，也可以在从鼠模型中获取实验性核医学数据集的情况下实现。针对正则化的Gauss-Newton方案和标准的非线性有界约束最小二乘算法进行了性能比较。