A Non-Convex Approach to Blind Calibration for Linear Random Sensing Models

Performing blind calibration is highly important in modern sensing strategies, particularly when calibration aided by multiple, accurately designed training signals is infeasible or resource-consuming. We here address it as a naturally-formulated non-convex problem for a linear model with sub-Gaussian ran- dom sensing vectors in which both the sensor gains and the sig- nal are unknown. A sample complexity bound is derived to as- sess that solving the problem by projected gradient descent with a suitable initialisation provably converges to the global optimum. These findings are supported by numerical evidence on the phase transition of blind calibration and by an imaging example