  We propose a scalable method to find a subspace $\widehat{\mathcal{H}}$ 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 $\widehat{\mathcal{C}} \subset \widehat{\mathcal{H}}$ 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
$\widehat{\mathcal{C}}$. 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.
