magni.cs.reconstruction.gamp package

Subpackage providing implementations of Generalised Approximate Message Passing (GAMP).

Routine listings

channel_initialisation
Module providing functionality for initialisations of GAMP channels.
config
Configger providing configuration options for this subpackage.
input_channel
Module providing GAMP input channels.
output_channel
Module providing GAMP output channels.
run(y, A, A_asq=None)
Run the GAMP reconstruction algorithm.
stop_criterion
Module providing GAMP stop criteria.

Notes

Implementations of Mimimum Mean Squared Error (MMSE) Generalised Approximate Message Passing (GAMP) from [1], [2] based on description of it in [3] are available. The GAMP is a generalisation of the Approximate Message Passing (AMP) algorithm derived independelty by Donoho et al. [4] and Krzakala et al. [5], [6].

This implementation allows custom input- and output channels as well as the use of sum approximations of the squared system matrix as detailed in [2], [5]. Furthermore, a simple damping option is available based on the description in [7] (see also [8] for more details on damping in GAMP).

References

[1]S. Rangan, “Generalized Approximate Message Passing for Estimation with Random Linear Mixing”, in IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, Jul. 31 - Aug. 5, 2011, pp. 2168-2172.
[2](1, 2) S. Rangan, “Generalized Approximate Message Passing for Estimation with Random Linear Mixing”, arXiv:1010.5141v2, pp. 1-22, Aug. 2012.
[3]J. T. Parker, “Approximate Message Passing Algorithms for Generalized Bilinear Inference”, PhD Thesis, Graduate School of The Ohio State University, 2014
[4]D.L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing”, Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 45, pp. 18914-18919, Nov. 2009.
[5](1, 2) F. Krzakala, M. Mezard, F. Sausset, Y. Sun, and L. Zdeborova, “Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices”, Journal of Statistical Mechanics: Theory and Experiment, vol. P08009, pp. 1-57, Aug. 2012.
[6]F. Krzakala, M. Mezard, F. Sausset, Y. Sun, and L. Zdeborova, “Statistical-Physics-Based Reconstruction in Compressed Sensing”, Physics Review X, vol. 2, no. 2, pp. (021005-1)-(021005-18), May 2012.
[7]S. Rangan, P. Schniter, and A. Fletcher. “On the Convergence of Approximate Message Passing with Arbitrary Matrices”, in IEEE International Symposium on Information Theory (ISIT), pp. 236-240, Honolulu, Hawaii, USA, Jun. 29 - Jul. 4, 2014.
[8]J. Vila, P. Schniter, S. Rangan, F. Krzakala, L. Zdeborova, “Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm”, in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), South Brisbane, Queensland, Australia, Apr. 19-24, 2015, pp. 2021-2025.