A scalable estimator of sets of integral operators

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 $\widehat \H$ 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 $\widehat \H$ in order to further reduce the search space. We provide theoretical guarantees on the estimators and a few numerical results.