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. |
Submodules¶
- magni.cs.reconstruction.gamp._algorithm module
- magni.cs.reconstruction.gamp._config module
- magni.cs.reconstruction.gamp.channel_initialisation module
- magni.cs.reconstruction.gamp.input_channel module
- magni.cs.reconstruction.gamp.output_channel module
- magni.cs.reconstruction.gamp.stop_criterion module