A scalable estimator of sets of integral operators. (13th September 2019)

• Record Type: Journal Article
• Authors: Debarnot, Valentin; Escande, Paul; Weiss, Pierre
• Is Part Of: Inverse problems. Volume 35:Number 10(2019)
• Publication Date: 2019-09-13
• Subjects: subspace learning -- blind inverse problems -- blind deblurring -- tensor decomposition; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab2fb3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The main objective of this work is to estimate a low dimensional subspace of operators in order to improve the identifiability of blind inverse problems. We propose a scalable method to find a subspace of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of tensor decomposition models, which was never used in this context. In addition, we propose to construct a convex subset of in order to further reduce the search space. We provide theoretical guarantees on the estimators and a few numerical results.