Joint super-resolution image reconstruction and parameter identification in imaging operator: analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging. (3rd December 2020)

• Record Type: Journal Article
• Authors: Kluth, Tobias; Bathke, Christine; Jiang, Ming; Maass, Peter
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: mathematical imaging -- hybrid models -- super-resolution -- joint parameter identification -- magnetic particle imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abc2fe
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.