Blind Calibration in Compressed Sensing using Message Passing Algorithms

Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central is- sue. In this paper we study the so-called blind calibration, i.e. when the training signals that are available to perform the calibration are sparse but unknown. We 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. Our algorithm is also applica- ble 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. We study numerically the phase diagram of the blind calibration problem, and show that even in cases where convex relaxation is pos- sible, our algorithm requires a smaller number of measurements and/or signals in order to perform well.

http://arxiv.org/abs/1306.4355

http://aspics.krzakala.org/

"Articles

* Our pionering paper on a new (and powerful) approach to compressed sensing is in open access on Phys. Rev. X 2, 021005 (2012) .
* A longer version, with many more details and computation, is now published on J. Stat. Mech. (2012) P08009 (and still avaliable on the arxiv).
* We have also investigated compressed sensing of signal which are only approximatly sparse . This was presented at the 50th Allerton conference.
* Another interesting case is when the matrix (and the signal) are binary. This has application in the Non-adaptive pooling strategies for detection of rare faulty items .
* Our more recent works deal with matrix uncertaintly and dictionnary learning and calibration.

Recent codes

Our new algorithm for Blind Sensor Calibration can be downloaded here in matlab. The corresponding article has been presented at NIPS 2013.

The Most recent matlab implementation of our algorithm for compressed sensing can be access on Github: BPCS (Belief Propagation for Compressed Sensing.

Older Codes and data

The original MATLAB implementaion can be download here. We would be more than happy to receive comments and suggestions.

We have also other older implementations: here is a c++ implementation . We have also a a python implementation if you prefer. The fastest implementation is the MATLAB one. Our solver has also been implemented in the KL1p library."