A conjugate gradient algorithm for blind sensor calibration in sparse recovery

This work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sensing. It aims to estimate the unknown complex gains at each sensor, given a set of measurements of some unknown training signals. We assume that the unknown training signals are all sparse. Instead of solving the problem by using convex 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 problem with a conjugate gradient method. Several numerical experiments are provided to oppose our approach to the solutions given by convex optimization and to demonstrate its performance.