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.
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