A Conjugate Gradient Algorithm for Blind Sensor Calibration in Sparse Recovery

International audienceThis work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sens- ing. It aims to estimate the unknown complex gains at each sensor, given a set of measurements of some unknown train- ing signals. We assume that the unknown training signals are all sparse. Instead of solving the problem by using con- vex optimization, we propose a cost function on a suitable manifold, namely, the set of complex diagonal matrices with determinant one. Such a construction can enhance numerical stabilities of the proposed algorithm. By exploring a global parameterization of the manifold, we tackle the BSC prob- lem with a conjugate gradient method. Several numerical experiments are provided to oppose our approach to the so- lutions given by convex optimization and to demonstrate its performance