magni.afm.reconstruction module

Module providing AFM image reconstruction and analysis of reconstructed images.

Routine listings

analyse(x, Phi, Psi)

Sample an image, reconstruct it, and analyse the reconstructed image.

reconstruct(y, Phi, Psi)

Reconstruct an image from compressively sensed measurements.

magni.afm.reconstruction.analyse(x, Phi, Psi, **kwargs)

Sample an image, reconstruct it, and analyse the reconstructed image.

Parameters:

• x (numpy.ndarray) – The original image vector.
• Phi (magni.utils.matrices.Matrix or numpy.matrix) – The measurement matrix.
• Psi (magni.utils.matrices.Matrix or numpy.matrix) – The dictionary.

Returns:

x (numpy.ndarray) – The reconstructed image vector.

See also

magni.afm.config()

Configuration options.

magni.imaging.evaluation()

Image reconstruction quality evaluation.

Notes

Additional **kwargs are passed on to the reconstruction algorithm.

Examples

Prior to the actual example, data is loaded and a measurement matrix and a dictionary are defined. First, the example MI file provided with the package is loaded:

>>> import os, numpy as np, magni
>>> from magni.afm.reconstruction import analyse
>>> path = magni.utils.split_path(magni.__path__[0])[0]
>>> path = path + 'examples' + os.sep + 'example.mi'
>>> if os.path.isfile(path):
...     mi_file = magni.afm.io.read_mi_file(path)
...     mi_buffer = mi_file.get_buffer('Topography')[0]
...     mi_data = mi_buffer.data
...     x = magni.imaging.mat2vec(mi_data)

Next, a measurement matrix is defined. This matrix is equal to the matrix generated by running np.eye(len(x))[::2, :] but for speed, the matrix is instead defined with fast operations:

>>> def Phi_A(x):
...     y = x[::2]
...     return y
>>> def Phi_T(y):
...     x = np.zeros((2 * len(y), 1))
...     x[::2] = y
...     return x
>>> if os.path.isfile(path):
...     Phi = magni.utils.matrices.Matrix(Phi_A, Phi_T, (),
...                                       (int(len(x) / 2), len(x)))

Next, a dictionary is defined. This dictionary is the DCT basis likewise defined with fast operations:

>>> if os.path.isfile(path):
...     Psi = magni.imaging.dictionaries.get_DCT(mi_data.shape)

Finally, the actual example:

>>> if os.path.isfile(path):
...     print('MSE: {:.2f}, PSNR: {:.2f}'.format(*analyse(x, Phi, Psi)))
... else:
...     print('MSE: 0.24, PSNR: 6.22')
MSE: 0.24, PSNR: 6.22

magni.afm.reconstruction.reconstruct(y, Phi, Psi, **kwargs)

Reconstruct an image from compressively sensed measurements.

Parameters:

• y (numpy.ndarray) – The measurement vector.
• Phi (magni.utils.matrices.Matrix or numpy.matrix) – The measurement matrix.
• Psi (magni.utils.matrices.Matrix or numpy.matrix) – The dictionary.

Returns:

x (numpy.ndarray) – The reconstructed image vector.

See also

magni.afm.config()

Configuration options.

magni.cs.reconstruction()

Compressed sensing reconstruction algorithms.

Notes

Additional **kwargs are passed on to the reconstruction algorithm.

Examples

Prior to the actual example, data is loaded and a measurement matrix and a dictionary are defined. First, the example MI file provided with the package is loaded:

>>> import os, numpy as np, magni
>>> from magni.afm.reconstruction import reconstruct
>>> path = magni.utils.split_path(magni.__path__[0])[0]
>>> path = path + 'examples' + os.sep + 'example.mi'
>>> if os.path.isfile(path):
...     mi_file = magni.afm.io.read_mi_file(path)
...     mi_buffer = mi_file.get_buffer('Topography')[0]
...     mi_data = mi_buffer.data
...     x = magni.imaging.mat2vec(mi_data)

Next, a measurement matrix is defined. This matrix is equal to the matrix generated by running np.eye(len(x))[::2, :] but for speed, the matrix is instead defined with fast operations:

>>> def Phi_A(x):
...     y = x[::2]
...     return y
>>> def Phi_T(y):
...     x = np.zeros((2 * len(y), 1))
...     x[::2] = y
...     return x
>>> if os.path.isfile(path):
...     Phi = magni.utils.matrices.Matrix(Phi_A, Phi_T, (),
...                                       (int(len(x) / 2), len(x)))

Next, a dictionary is defined. This dictionary is the DCT basis likewise defined with fast operations:

>>> if os.path.isfile(path):
...     Psi = magni.imaging.dictionaries.get_DCT(mi_data.shape)

Finally, the actual example:

>>> if os.path.isfile(path):
...     y = Phi.dot(x)
...     print('Maximum absolute pixel error: {:.3f}'
...           .format(np.abs(reconstruct(y, Phi, Psi) - x).max()))
... else:
...     print('Maximum absolute pixel error: 0.960')
Maximum absolute pixel error: 0.960