Blind Calibration in Compressed Sensing Using Message Passing Algorithms
In this paper the authors study the so-called blind calibration, i.e. when the training signals that are available to perform the calibration are sparse but unknown. They extend the Approximate Message Passing (AMP) algorithm used in CS to the case of blind calibration. In the calibration-AMP, both the gains on the sensors and the elements of the signals are treated as unknowns. Their algorithm is also applicable to settings in which the sensors distort the measurements in other ways than multiplication by a gain, unlike previously suggested blind calibration algorithms based on convex relaxations.