magni.cs.reconstruction.gamp.output_channel module¶
Module providing output channel functions for the Generalised Approximate Message Passing (GAMP) algorithm.
Routine listings¶
- ValidatedMMSEOutputChannel(magni.utils.validation.types.MMSEOutputChannel)
- A base class for validated
magni.cs.reconstruction.gamp
output channels. - AWGN(ValidatedMMSEOutputChannel)
- An Additive White Gaussian Noise (AWGN) MMSE output channel.
-
class
magni.cs.reconstruction.gamp.output_channel.
ValidatedMMSEOutputChannel
(var)[source]¶ Bases:
magni.utils.validation.types.MMSEOutputChannel
A base class for validated
magni.cs.reconstruction.gamp
output channels.Parameters: var (dict) – The output channel state variables. -
compute
(var)[source]¶ Compute the output channel value.
Parameters: var (dict) – The variables used in computing of the output channel value. Returns: - mean (ndarray) – The computed output channel mean.
- variance (ndarray) – The computed output channel variance.
Notes
This method honors magni.utils.validation.enable_allow_validate_once.
-
-
class
magni.cs.reconstruction.gamp.output_channel.
AWGN
(var)[source]¶ Bases:
magni.cs.reconstruction.gamp.output_channel.ValidatedMMSEOutputChannel
An Additive White Gaussian Noise (AWGN) MMSE output channel.
This channel is based on equations (41), (42), and (43) in [1] and allows for using Expectation Maximization (EM) for learning the channel parameter as detailed in equation (77) in [2] (see also [2] for an introduction to EM for GAMP).
Parameters: - sigma_sq (float or int) – The noise level variance (initial noise level when the noise level is estimated).
- noise_level_estimation (str) – The method used for estimating (learning) the noise level in each iteration.
Notes
The above Parameters are the output channel parameters that must be passed in a var dict to the channel constructor.
Possible values for noise_level_estimation are:
- ‘sample_variance’ - Estimate noise level using the sample variance.
- ‘median’ - Estimate noise level from the median.
- ‘em’ - Estimate noise using Expectation Maximization (EM).
- ‘fixed’ - Use a fixed noise level in all iterations.
References
[1] S. Rangan, “Generalized Approximate Message Passing for Estimation with Random Linear Mixing”, arXiv:1010.5141v2, pp. 1-22, Aug. 2012. [2] (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. [3] J. P. Vila and P. Schniter, “Expectation-Maximization Gaussian-Mixture Approximate Message Passing”, IEEE Transactions on Signal Processing, 2013, vol. 61, no. 19, pp. 4658-4672, Oct. 2013.