magni.cs.reconstruction.amp.util module¶
Module providing utilities for the Approximate Message Passing (AMP) algorithm.
Routine listings¶
- theta_mm(theta)
- Return the minimax optimal value of the AMP theta tunable parameter.
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magni.cs.reconstruction.amp.util.
theta_mm
(delta)[source]¶ Return the minimax optimal value of the AMP theta tunable parameter.
A simple lookup table is used to determine the minimax optimal value of the AMP theta tunable parameter as specified in [1]. Specifically, the formula in the top left column on page 6 is used without the 1/sqrt(delta) factor (as specfified in the SI Appendix) and with kappa=2.
Parameters: delta (float) – The undersampling ratio. Returns: theta_mm (float) – The minimax optimal value of the theta parameter. References
[1] 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, p. 18914-18919, Nov. 2009. Examples
For example, get the optimal parameters for a few undersampling ratios
>>> from magni.cs.reconstruction.amp.util import theta_mm >>> theta_mm(0.1) 1.736 >>> theta_mm(0.2121) 1.378 >>> theta_mm(0.001) 3.312 >>> theta_mm(0.999) 0.032 >>> theta_mm(0.0001) 3.312 >>> theta_mm(0.99999) 0.032