dicodile.dicodile¶

dicodile.dicodile(X, D_init, reg=0.1, n_iter=100, eps=1e-05, window=False, z_positive=True, n_workers=4, w_world='auto', tol=0.001, hostfile=None, dicod_kwargs={}, random_state=None, verbose=0)¶

Convolutional dictionary learning.

Computes a sparse representation of a signal X, returning a dictionary D and a sparse activation signal Z such that X is close to \(Z \ast D\).

This is done by solving the following optimization problem:

\[\underset{Z,D, \left \| D_{k}\right \|\leq 1}{min} \frac{1}{2} \left \| X - Z \ast D \right\|_{2}^{2} + \lambda \left \| Z \right \|_{1}\]

The support for X is noted sig_support.

The support for D is noted atom_support.

Parameters:

Xndarray, shape (n_channels, *sig_support)

Signal to encode.

For example, a 3-channel RGB image of definition 640x480 would have a shape of (3, 640, 480), a grayscale image of the same definition would have a shape of (1, 640, 480), a single time series would have a shape of (1, number_of_samples)

D_initndarray, shape (n_atoms, n_channels, *atom_support)

Current atoms dictionary.

regfloat, defaults to .1

Regularization parameter, in [0,1] The λ parameter is computed as reg * lambda_max

n_iterint, defaults to 100

Maximum number of iterations

epsfloat, defaults to 1e-5

Tolerance for the stopping criterion. A lower value will result in more computing time.

windowbool

If set to True, the learned atoms are multiplied by a Tukey window that sets its borders to 0. This can help having patterns localized in the middle of the atom support and reduces border effects.

z_positivebool, default True

If True, adds a constraint that the activations Z must be positive.

n_workersint, defaults to 4

Number of workers used to compute the convolutional sparse coding solution.

w_worldint or {{‘auto’}}

Number of jobs used per row in the splitting grid. This should divide n_workers.

tolfloat, defaults to 1e-3

Tolerance for minimal update size.

hostfilestr or None

MPI hostfile as used by mpirun. See your MPI implementation documentation. Defaults to None.

dicod_kwargsdict

Extra arguments passed to the dicod function. See dicodile.update_z.dicod

random_stateNone or int or RandomState

Random state to seed the random number generator.

verboseint, defaults to 0

Verbosity level, higher is more verbose.

Returns:

D_hatndarray, shape (n_channels, *sig_support): Updated atoms dictionary.
Z_hatndarray, shape (n_channels, *valid_support): Activations of the different atoms (where or when the atoms are estimated).
pobjlist of float: list of costs
timeslist of float: list of running times (seconds) for each dictionary and activation update step. The total running time of the algorithm is given by sum(times)