from cuqi.implicitprior import RegularizedGaussian
from cuqi.distribution import Distribution, GMRF
[docs]
class RegularizedGMRF(RegularizedGaussian):
""" Implicit Regularized GMRF (Gaussian Markov Random Field).
Defines a so-called implicit prior based on a GMRF distribution with implicit regularization.
The regularization can be defined in the form of a proximal operator or a projector.
Alternatively, preset constraints and regularization can be used.
Only one of proximal, projector, constraint or regularization can be provided. Otherwise, an error is raised.
Can be used as a prior in a posterior which can be sampled with the RegularizedLinearRTO sampler.
For more details on implicit regularized Gaussian see the following paper:
[1] Everink, Jasper M., Yiqiu Dong, and Martin S. Andersen. "Sparse Bayesian inference with regularized
Gaussian distributions." Inverse Problems 39.11 (2023): 115004.
Parameters
----------
mean
See :class:`~cuqi.distribution.GMRF` for details.
prec
See :class:`~cuqi.distribution.GMRF` for details.
bc_type
See :class:`~cuqi.distribution.GMRF` for details.
order
See :class:`~cuqi.distribution.GMRF` for details.
proximal : callable f(x, scale) or None
Euclidean proximal operator f of the regularization function g, that is, a solver for the optimization problem
min_z 0.5||x-z||_2^2+scale*g(x).
projector : callable f(x) or None
Euclidean projection onto the constraint C, that is, a solver for the optimization problem
min_(z in C) 0.5||x-z||_2^2.
constraint : string or None
Preset constraints. Can be set to "nonnegativity" and "box". Required for use in Gibbs.
For "box", the following additional parameters can be passed:
lower_bound : array_like or None
Lower bound of box, defaults to zero
upper_bound : array_like
Upper bound of box, defaults to one
regularization : string or None
Preset regularization. Can be set to "l1". Required for use in Gibbs in future update.
For "l1" or "tv", the following additional parameters can be passed:
strength : scalar
Regularization parameter, i.e., strength*||Lx||_1, defaults to one
"""
[docs]
def __init__(self, mean=None, prec=None, bc_type='zero', order=1, proximal = None, projector = None, constraint = None, regularization = None, **kwargs):
args = {"lower_bound" : kwargs.pop("lower_bound", None),
"upper_bound" : kwargs.pop("upper_bound", None),
"strength" : kwargs.pop("strength", None)}
# Underlying explicit GMRF
self._gaussian = GMRF(mean, prec, bc_type=bc_type, order=order, **kwargs)
kwargs.pop("geometry", None)
# Init from abstract distribution class
super(Distribution, self).__init__(**kwargs)
self._force_list = False
self._parse_regularization_input_arguments(proximal, projector, constraint, regularization, args)
[docs]
class ConstrainedGMRF(RegularizedGMRF):
""" Implicit Constrained GMRF (Gaussian Markov Random Field).
Defines a so-called implicit prior based on a GMRF distribution with implicit constraints.
The constraint can be defined as a preset or in the form of a projector.
Precisely one of projector or constraint needs to be provided. Otherwise, an error is raised.
Can be used as a prior in a posterior which can be sampled with the RegularizedLinearRTO sampler.
Alias for :class:`~cuqi.implicitprior.RegularizedGMRF` with only constraints available.
For more details on implicit regularized Gaussian see the following paper:
[1] Everink, Jasper M., Yiqiu Dong, and Martin S. Andersen. "Sparse Bayesian inference with regularized
Gaussian distributions." Inverse Problems 39.11 (2023): 115004.
Parameters
----------
mean
See :class:`~cuqi.distribution.GMRF` for details.
prec
See :class:`~cuqi.distribution.GMRF` for details.
bc_type
See :class:`~cuqi.distribution.GMRF` for details.
order
See :class:`~cuqi.distribution.GMRF` for details.
projector : callable f(x) or None
Euclidean projection onto the constraint C, that is, a solver for the optimization problem
min_(z in C) 0.5||x-z||_2^2.
constraint : string or None
Preset constraints. Can be set to "nonnegativity" and "box". Required for use in Gibbs.
For "box", the following additional parameters can be passed:
lower_bound : array_like or None
Lower bound of box, defaults to zero
upper_bound : array_like
Upper bound of box, defaults to one
"""
[docs]
def __init__(self, mean=None, prec=None, bc_type='zero', order=1, projector=None, constraint=None, **kwargs):
super().__init__(mean=mean, prec=prec, bc_type=bc_type, order=order, projector=projector, constraint=constraint, **kwargs)
[docs]
class NonnegativeGMRF(RegularizedGMRF):
""" Implicit Nonnegative GMRF (Gaussian Markov Random Field).
Defines a so-called implicit prior based on a GMRF distribution with implicit nonnegativity constraints.
Can be used as a prior in a posterior which can be sampled with the RegularizedLinearRTO sampler.
Alias for :class:`~cuqi.implicitprior.RegularizedGMRF` with only nonnegativity constraints.
For more details on implicit regularized Gaussian see the following paper:
[1] Everink, Jasper M., Yiqiu Dong, and Martin S. Andersen. "Sparse Bayesian inference with regularized
Gaussian distributions." Inverse Problems 39.11 (2023): 115004.
Parameters
----------
mean
See :class:`~cuqi.distribution.GMRF` for details.
prec
See :class:`~cuqi.distribution.GMRF` for details.
bc_type
See :class:`~cuqi.distribution.GMRF` for details.
order
See :class:`~cuqi.distribution.GMRF` for details.
"""
[docs]
def __init__(self, mean=None, prec=None, bc_type='zero', order=1, **kwargs):
super().__init__(mean=mean, prec=prec, bc_type=bc_type, order=order, constraint="nonnegativity", **kwargs)
