Abstract
The Aharonov–Bohm effect is a well‐established quantum phenomenon that relates the behaviour of an electron not only to the local electromagnetic field but also to the associated potentials. An important consequence is that electron beams travelling through an arbitrary medium can carry information not only about the properties of the materials along with their trajectories but also about those of the entire background around them. Based on this established principle, the authors propose an inverse formulation for the estimation of a sample's magnetic permeability based on measurements of the wave function of a split electron beam. For one‐dimensional distributions, the analysed concept is shown to lead to the ideal retrieval of the sample's texture for a sufficiently large number of measurements. Two‐ and three‐dimensional permeability distributions can be successfully estimated by employing sparsification transformations associated with compressive imaging approaches. The proposed configuration and formulation may be useful in non‐destructive detection and sensing of biological, chemical or ferrimagnetic samples.