Computed tomography with view angle estimation using uncertainty quantification. (7th June 2021)

• Record Type: Journal Article
• Authors: Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian
• Is Part Of: Inverse problems. Volume 37:Number 6(2021)
• Publication Date: 2021-06-07
• Subjects: computed tomography -- view angle estimation -- uncertainty quantification -- block representation -- alternating updates; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abf5ba
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider computed tomography (CT) with uncertain measurement geometry, with a focus on the case where the view angles are uncertain and where estimation of these angles improves the reconstruction. We propose a new reconstruction model and a corresponding algorithm that has an additional view-angle estimation component, allowing us to determine the angles solely from the measured CT data. A key component of our approach is that we quantify the uncertainty of the view angles via a model-discrepancy formulation, allowing us to take the uncertainty into account in the image reconstruction. This approach generalizes in a straightforward way to other cases of uncertain geometry. Our method is computationally efficient since we can utilize a block-structure of the computational problem for estimation of both the CT image and the view angles under the assumption that the view angles are independent. The joint image/angle reconstruction problem is non-convex which leads to difficulties in recently proposed algorithms, and we demonstrate numerically that our method seems to avoid these difficulties. Simulations show that our method, with a total variation prior that reflects our phantoms, is able to achieve reconstructions whose quality is similar to ones obtained with the correct view angles (the ideal scenario).