论文标题
成像运算符中的联合超分辨率图像重建和参数识别：双线性操作员方程，数值解决方案和应用于磁性粒子成像的分析
Joint super-resolution image reconstruction and parameter identification in imaging operator: Analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging
论文作者
论文摘要
成像方式和相关应用的一项重要特性是分辨出依赖各种因素（例如仪器或数据处理）的图像重建。分辨率的限制可以具有多种存在的起源，例如，可用数据的分辨率有限，数据中的噪声水平和/或不精确的模型运算符。在这项工作中，我们研究了一种适合不应收入机模型运算符的新型数据处理方法。在这里，在混合方法中包括两个不同的信息源，高维模型信息和较低分辨率的高质量测量。高分辨率图像的关节重建和成像算子的参数是通过最小化Tikhonov型函数来获得的。对于稳定性，收敛和收敛速率，分析了双线性操作员方程的混合方法。我们进一步得出了利用代数重建技术的算法解决方案。这项研究的数值结果从学术测试案例到磁性粒子成像中的图像重建范围都得到了补充。
One important property of imaging modalities and related applications is the resolution of image reconstructions which relies on various factors such as instrumentation or data processing. Restrictions in resolution can have manifold origins, e.g., limited resolution of available data, noise level in the data, and/or inexact model operators. In this work we investigate a novel data processing approach suited for inexact model operators. Here, two different information sources, high-dimensional model information and high-quality measurement on a lower resolution, are comprised in a hybrid approach. The joint reconstruction of a high resolution image and parameters of the imaging operator are obtained by minimizing a Tikhonov-type functional. The hybrid approach is analyzed for bilinear operator equations with respect to stability, convergence, and convergence rates. We further derive an algorithmic solution exploiting an algebraic reconstruction technique. The study is complemented by numerical results ranging from an academic test case to image reconstruction in magnetic particle imaging.
