A Conjugate Gradient Algorithm For Blind Sensor Calibration In Sparse Recovery
Hao Shen, Martin Kleinsteuber, Cagdas Bilen, Remi Gribonval

Abstract:
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 on 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.