Representation and reconstruction of covariance operators in linear inverse problems. (20th August 2020)

• Record Type: Journal Article
• Authors: Lila, Eardi; Arridge, Simon; Aston, John A D
• Is Part Of: Inverse problems. Volume 36:Number 8(2020)
• Publication Date: 2020-08-20
• Subjects: inverse problems -- covariance operator -- principal component analysis -- dynamic functional connectivity -- magnetoencephalography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab8713
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The proposed methodology can be applied either to the analysis of indirectly observed functional images or to the associated covariance operators, representing second-order information, and thus lying on a non-Euclidean space. To deal with the ill-posedness of the inverse problem, we exploit the spatial structure of the sample data by introducing a flexible regularizing term embedded in the model. Thanks to its efficiency, the proposed model is applied to MEG data, leading to a novel approach to the investigation of functional connectivity.