A Non-Convex Blind Calibration Method for Randomised Sensing Strategies

TL;DR

This paper introduces a non-convex blind calibration method for random sensing strategies that uses projected gradient descent to recover signals without training, demonstrating convergence under certain conditions.

Contribution

It proposes a novel non-convex optimization approach for blind calibration in linear random sensing models, with theoretical convergence guarantees.

Findings

Algorithm converges to the global optimum under sample complexity conditions.

Numerical experiments show effective blind calibration of sensor gains.

Method simplifies calibration in computational sensing applications.

Abstract

The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not require any training, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each of which is subject to an unknown multiplicative factor (gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable initialisation. An analysis of this algorithm allows us to show that it converges to the global optimum provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Finally, we present some numerical experiments in which our algorithm allows for a simple solution to blind calibration of sensor gains in computational sensing applications.