A scalable estimator of sets of integral operators

We propose a scalable method to find a subspace widehatH of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of the Tucker-2 decomposition model, which was never used in this context. In addition, we propose to construct a convex set widehatC subset widehatH as the convex hull of the observed operators. It is a minimax optimal estimator under the Nikodym metric. We then provide an efficient algorithm to compute projection on widehatC. We observe a good empirical behavior of the method in simulations. The main aim of this work is to improve the identifiability of complex linear operators in blind inverse problems.