magni.cs.reconstruction.iht package

Subpackage providing an implementation of Iterative Hard Thresholding (IHT).

Note

Deprecated in Magni 1.3.0. magni.cs.reconstruction.iht will be removed in a future version. Use the more general magni.cs.reconstruction.it instead.

Warning

Change of variable interpretation. In magni.cs.reconstruction.it the config variable threshold_fixed has a different interpretation than in magni.cs.reconstruction.iht.

Routine listings

config
Configger providing configuration options for this subpackage.
run(y, A)
Run the IHT reconstruction algorithm.

Notes

The IHT reconstruction algorithm is described in [1]. The default configuration uses the False Alarm Rate heuristic described in [2].

References

[1]T. Blumensath and M.E. Davies, “Iterative Thresholding for Sparse Approximations”, Journal of Fourier Analysis and Applications, vol. 14, pp. 629-654, Sep. 2008.
[2]A. Maleki and D.L. Donoho, “Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing”, IEEE Journal Selected Topics in Signal Processing, vol. 3, no. 2, pp. 330-341, Apr. 2010.
magni.cs.reconstruction.iht.run(y, A)[source]

Run the IHT reconstruction algorithm.

Note

Deprecated in Magni 1.3.0 magni.cs.reconstruction.iht will be removed in a future version. Use the more general magni.cs.reconstruction.it instead.

Parameters:
  • y (ndarray) – The m x 1 measurement vector.
  • A (ndarray) – The m x n matrix which is the product of the measurement matrix and the dictionary matrix.
Returns:

alpha (ndarray) – The n x 1 reconstructed coefficient vector.

Examples

For example, recovering a vector from random measurements

>>> import warnings
>>> import numpy as np
>>> from magni.cs.reconstruction.iht import run, config
>>> np.random.seed(seed=6021)
>>> A = 1 / np.sqrt(80) * np.random.randn(80, 200)
>>> alpha = np.zeros((200, 1))
>>> alpha[:10] = 1
>>> y = A.dot(alpha)
>>> with warnings.catch_warnings():
...     warnings.simplefilter('ignore')
...     alpha_hat = run(y, A)
...
>>> np.set_printoptions(suppress=True)
>>> alpha_hat[:12]
array([[ 0.99836297],
       [ 1.00029086],
       [ 0.99760224],
       [ 0.99927175],
       [ 0.99899124],
       [ 0.99899434],
       [ 0.9987368 ],
       [ 0.99801849],
       [ 1.00059408],
       [ 0.9983772 ],
       [ 0.        ],
       [ 0.        ]])
>>> (np.abs(alpha_hat) > 1e-2).sum()
10

Or recovering the same only using a fixed threshold level:

>>> config.update({'threshold': 'oracle', 'threshold_fixed': 10./80})
>>> with warnings.catch_warnings():
...     warnings.simplefilter('ignore')
...     alpha_hat_2 = run(y, A)
...
>>> alpha_hat_2[:12]
array([[ 0.99877706],
       [ 0.99931441],
       [ 0.9978366 ],
       [ 0.99944973],
       [ 1.00052762],
       [ 1.00033436],
       [ 0.99943286],
       [ 0.99952526],
       [ 0.99941578],
       [ 0.99942908],
       [ 0.        ],
       [ 0.        ]])

>>> (np.abs(alpha_hat_2) > 1e-2).sum()
10