Reduced-Space Relevance Vector Machine for Adaptive Electrical Capacitance Volume Tomography

We introduce an efficient synthetic electrode selection strategy for use in Adaptive Electrical Capacitance Volume Tomography (AECVT). The proposed strategy is based on the Adaptive Relevance Vector Machine (ARVM) method and allows to successively obtain synthetic electrode configurations that yield the most decrease in the image reconstruction uncertainty for the spatial distribution of the permittivity in the region of interest. The problem is first formulated as an instance of the Quadratic Unconstrained Binary Optimization (QUBO). By noting that the QUBO formulation is an NP-hard problem and thus prohibitive in practice, we then introduce the Reduced ARVM method, corresponding to the application of the ARVM method to a reduced search space. By using the Reduced ARVM method, good image reconstruction and low uncertainty levels can be achieved in AECVT with considerably fewer measurements. To corroborate our analysis, we present simulation results for three representative AECVT scenarios.