Compressive Signal Recovery Under Sensing Matrix Errors Combined With Unknown Measurement Gains

Compressed Sensing assumes a linear model for acquiring signals however imperfections may arise in the specification of the ‘ideal’ measurement model. We present the first study which considers the case of two such common calibration issues: (a) unknown measurement scaling (sensor gains) due to hardware vagaries or due to unknown object motion in MRI scanning, in conjunction with (b) unknown offsets to measurement frequencies in case of a Fourier measurement matrix. We propose an alternating minimisation algorithm for on-the-fly signal recovery in the case when errors (a) and (b) occur jointly. We show simulation results over a variety of situations that outperform the baselines of signal recovery by ignoring either or both types of calibration errors. We also show theoretical results for signal recovery by introducing a perturbed version of the well-known Generalized Multiple Measurement Vectors (GMMV) model.