Blind Sensor Calibration using Approximate Message Passing
  The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them on real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal ac- quisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measures. Cal-AMP shares the scalability of approximate message passing, allowing to treat big sized instances of these problems, and ex- perimentally exhibits a phase transition between domains of success and failure. 
Christophe Sch\"ulke, Francesco Caltagirone and Lenka Zdeborov\'a
cs.IT math.IT