tick.prox.ProxTV

class tick.prox.ProxTV(strength: float, range: tuple = None, positive: bool = False)[source]

Proximal operator of the total-variation penalization

Parameters

strength : float

Level of total-variation penalization

range : tuple of two int, default=`None`

Range on which the prox is applied. If None then the prox is applied on the whole vector

positive : bool, default=`False`

If True, apply L1 penalization together with a projection onto the set of vectors with non-negative entries

Attributes

dtype : {'float64', 'float32'}

Type of the arrays used.

Notes

Uses the fast-TV algorithm described in:

  • “A Direct Algorithm for 1D Total Variation Denoising” by Laurent Condat, Ieee Signal Proc. Letters

__init__(strength: float, range: tuple = None, positive: bool = False)[source]

Initialize self. See help(type(self)) for accurate signature.

call(coeffs, step=1.0, out=None)

Apply proximal operator on a vector. It computes:

\[argmin_x \big( f(x) + \frac{1}{2} \|x - v\|_2^2 \big)\]
Parameters

coeffs : numpy.ndarray, shape=(n_coeffs,)

Input vector on which is applied the proximal operator

step : float or np.array, default=1.

The amount of penalization is multiplied by this amount

  • If float, the amount of penalization is multiplied by this amount

  • If np.array, then each coordinate of coeffs (within the given range), receives an amount of penalization multiplied by t (available only for separable prox)

out : numpy.ndarray, shape=(n_params,), default=None

If not None, the output is stored in the given out. Otherwise, a new vector is created.

Returns

output : numpy.ndarray, shape=(n_coeffs,)

Same object as out

Notes

step must have the same size as coeffs whenever range is None, or a size matching the one given by the range otherwise

value(coeffs: numpy.ndarray)[source]

Returns the value of the penalization at coeffs

Parameters

coeffs : numpy.ndarray, shape=(n_coeffs,)

The value of the penalization is computed at this point

Returns

output : float

Value of the penalization at coeffs