# -*- coding: utf-8 -*-
r"""
The :mod:`pygsp.optimization` module provides tools to solve convex
optimization problems on graphs.
"""
from pygsp import utils
logger = utils.build_logger(__name__)
def _import_pyunlocbox():
try:
from pyunlocbox import functions, solvers
except Exception as e:
raise ImportError('Cannot import pyunlocbox, which is needed to solve '
'this optimization problem. Try to install it with '
'pip (or conda) install pyunlocbox. '
'Original exception: {}'.format(e))
return functions, solvers
[docs]def prox_tv(x, gamma, G, A=None, At=None, nu=1, tol=10e-4, maxit=200, use_matrix=True):
r"""
Total Variation proximal operator for graphs.
This function computes the TV proximal operator for graphs. The TV norm
is the one norm of the gradient. The gradient is defined in the
function :meth:`pygsp.graphs.Graph.grad`.
This function requires the PyUNLocBoX to be executed.
This function solves:
:math:`sol = \min_{z} \frac{1}{2} \|x - z\|_2^2 + \gamma \|x\|_{TV}`
Parameters
----------
x: int
Input signal
gamma: ndarray
Regularization parameter
G: graph object
Graphs structure
A: lambda function
Forward operator, this parameter allows to solve the following problem:
:math:`sol = \min_{z} \frac{1}{2} \|x - z\|_2^2 + \gamma \| A x\|_{TV}`
(default = Id)
At: lambda function
Adjoint operator. (default = Id)
nu: float
Bound on the norm of the operator (default = 1)
tol: float
Stops criterion for the loop. The algorithm will stop if :
:math:`\frac{n(t) - n(t - 1)} {n(t)} < tol`
where :math:`n(t) = f(x) + 0.5 \|x-y\|_2^2` is the objective function at iteration :math:`t`
(default = :math:`10e-4`)
maxit: int
Maximum iteration. (default = 200)
use_matrix: bool
If a matrix should be used. (default = True)
Returns
-------
sol: solution
Examples
--------
"""
if A is None:
def A(x):
return x
if At is None:
def At(x):
return x
tight = 0
l1_nu = 2 * G.lmax * nu
if use_matrix:
def l1_a(x):
return G.Diff * A(x)
def l1_at(x):
return G.Diff * At(D.T * x)
else:
def l1_a(x):
return G.grad(A(x))
def l1_at(x):
return G.div(x)
functions, _ = _import_pyunlocbox()
functions.norm_l1(x, gamma, A=l1_a, At=l1_at, tight=tight, maxit=maxit, verbose=verbose, tol=tol)