A scalable estimator of sets of integral operators

Abstract

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

References in corpus (1)

• Optimal Sample Complexity for Blind Gain and Phase Calibration

Cited by in corpus (1)

• Joint Cryo-ET Alignment and Reconstruction with Neural Deformation Fields