dival.reconstructors.odl_reconstructors module

Provides wrappers for reconstruction methods of odl.

class dival.reconstructors.odl_reconstructors.FBPReconstructor(ray_trafo, padding=True, hyper_params=None, pre_processor=None, post_processor=None, recompute_fbp_op=True, **kwargs)[source]

Bases: Reconstructor

HYPER_PARAMS = {'filter_type': {'choices': ['Ram-Lak', 'Shepp-Logan', 'Cosine', 'Hamming', 'Hann'], 'default': 'Ram-Lak'}, 'frequency_scaling': {'default': 1.0, 'grid_search_options': {'num_samples': 11}, 'range': [0, 1]}}

Reconstructor applying filtered back-projection.

fbp_op

The operator applying filtered back-projection. It is computed in the constructor, and is recomputed for each reconstruction if recompute_fbp_op == True (since parameters could change).

Type:

odl.operator.Operator

__init__(ray_trafo, padding=True, hyper_params=None, pre_processor=None, post_processor=None, recompute_fbp_op=True, **kwargs)[source]
Parameters:

  • ray_trafo (odl.tomo.operators.RayTransform) – The forward operator. See odl.tomo.fbp_op for details.

  • padding (bool, optional) – Whether to use padding (the default is True). See odl.tomo.fbp_op for details.

  • pre_processor (callable, optional) – Callable that takes the observation and returns the sinogram that is passed to the filtered back-projection operator.

  • post_processor (callable, optional) – Callable that takes the filtered back-projection and returns the final reconstruction.

  • recompute_fbp_op (bool, optional) – Whether fbp_op should be recomputed on each call to reconstruct(). Must be True (default) if changes to ray_trafo, hyper_params or padding are planned in order to use the updated values in reconstruct(). If none of these attributes will change, you may specify recompute_fbp_op==False, so fbp_op can be computed only once, improving reconstruction time efficiency.

property filter_type
property frequency_scaling
class dival.reconstructors.odl_reconstructors.CGReconstructor(op, x0, niter=None, callback=None, op_is_symmetric=False, **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying the conjugate gradient method.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

op_is_symmetric

If False (default), the normal equations are solved. If True, op is assumed to be self-adjoint and the system of equations is solved directly.

Type:

bool

__init__(op, x0, niter=None, callback=None, op_is_symmetric=False, **kwargs)[source]

Calls odl.solvers.iterative.iterative.conjugate_gradient_normal (if op_is_symmetric == False) or odl.solvers.iterative.iterative.conjugate_gradient (if op_is_symmetric == True).

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem. If op_is_symmetric == False (default), the call op.derivative(x).adjoint must be valid. If op_is_symmetric == True, op must be linear and self-adjoint.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

  • op_is_symmetric (bool, optional) – If False (default), the normal equations are solved. If True, op is required to be self-adjoint and the system of equations is solved directly.

property iterations
class dival.reconstructors.odl_reconstructors.GaussNewtonReconstructor(op, x0, niter=None, zero_seq_gen=None, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying the Gauss-Newton method.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Maximum number of iterations.

Type:

int

zero_seq_gen

Zero sequence generator used for regularization.

Type:

generator

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, zero_seq_gen=None, callback=None, **kwargs)[source]

Calls odl.solvers.iterative.iterative.gauss_newton.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem. The call op.derivative(x).adjoint must be valid.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Maximum number of iterations (overriding self.hyper_params["iterations"] initially).

  • zero_seq_gen (generator, optional) – Zero sequence generator used for regularization. Default: generator yielding 2^(-i).

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.KaczmarzReconstructor(ops, x0, niter=None, omega=1, random=False, projection=None, callback=None, callback_loop='outer', **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying Kaczmarz’s method.

ops

The forward operators of the inverse problem.

Type:

sequence of odl.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

omega

Relaxation parameter. If a single float is given it is used for all operators.

Type:

positive float or sequence of positive floats

random

Whether the order of the operators is randomized in each iteration.

Type:

bool

projection

Callable that can be used to modify the iterates in each iteration.

Type:

callable

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

callback_loop

Whether the callback should be called in the inner or outer loop.

Type:

{‘inner’, ‘outer’}

__init__(ops, x0, niter=None, omega=1, random=False, projection=None, callback=None, callback_loop='outer', **kwargs)[source]

Calls odl.solvers.iterative.iterative.kaczmarz.

Parameters:

  • ops (sequence of odl.Operator) – The forward operators of the inverse problem. The call ops[i].derivative(x).adjoint must be valid for all i.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • omega (positive float or sequence of positive floats, optional) – Relaxation parameter. If a single float is given it is used for all operators.

  • random (bool, optional) – Whether the order of the operators is randomized in each iteration.

  • projection (callable, optional) – Callable that can be used to modify the iterates in each iteration.

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

  • callback_loop ({'inner', 'outer'}) – Whether the callback should be called in the inner or outer loop.

property iterations
class dival.reconstructors.odl_reconstructors.LandweberReconstructor(op, x0, niter=None, omega=None, projection=None, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying Landweber’s method.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

omega

Relaxation parameter.

Type:

positive float

projection

Callable that can be used to modify the iterates in each iteration.

Type:

callable

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, omega=None, projection=None, callback=None, **kwargs)[source]

Calls odl.solvers.iterative.iterative.landweber.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem. The call op.derivative(x).adjoint must be valid.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • omega (positive float, optional) – Relaxation parameter.

  • projection (callable, optional) – Callable that can be used to modify the iterates in each iteration. One argument is passed and expected be modified in-place.

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.MLEMReconstructor(op, x0, niter=None, noise='poisson', callback=None, sensitivities=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying Maximum Likelihood Expectation Maximization.

If multiple operators are given, Ordered Subsets MLEM is applied.

op

The forward operator(s) of the inverse problem.

Type:

odl.operator.Operator or sequence of odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

noise

Noise model determining the variant of MLEM.

Type:

{‘poisson’} or None

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

sensitivities

Usable with noise='poisson'. The algorithm contains an A^T 1 term, if this parameter is given, it is replaced by it. Default: op[i].adjoint(op[i].range.one())

Type:

float or op.domain element-like

__init__(op, x0, niter=None, noise='poisson', callback=None, sensitivities=None, **kwargs)[source]

Calls odl.solvers.iterative.statistical.osmlem.

Parameters:

  • op (odl.operator.Operator or sequence of odl.operator.Operator) – The forward operator(s) of the inverse problem. If an operator sequence is given, Ordered Subsets MLEM is applied.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • noise ({'poisson'}, optional) – Noise model determining the variant of MLEM. For 'poisson', the initial value of x should be non-negative.

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

  • sensitivities (float or op.domain element-like, optional) – Usable with noise='poisson'. The algorithm contains an A^T 1 term, if this parameter is given, it is replaced by it. Default: op[i].adjoint(op[i].range.one())

property iterations
class dival.reconstructors.odl_reconstructors.ISTAReconstructor(op, x0, niter=None, gamma=0.001, reg=<class 'odl.solvers.functional.default_functionals.L1Norm'>, accelerated=True, lam=1.0, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Iterative reconstructor applying proximal gradient algorithm for convex optimization, also known as Iterative Soft-Thresholding Algorithm (ISTA).

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

gamma

Step size parameter.

Type:

positive float

reg

The regularization operator of the inverse problem. Needs to have f.proximal.

Type:

odl.solvers.functional.Functional

accelerated

Indicates which algorithm to use. If False, then the “Iterative Soft-Thresholding Algorithm” (ISTA) is used. If True, then the accelerated version FISTA is used.

Type:

boolean

lam

Overrelaxation step size (default 1.0). If callable, it should take an index (starting at zero) and return the corresponding step size.

Type:

float or callable

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, gamma=0.001, reg=<class 'odl.solvers.functional.default_functionals.L1Norm'>, accelerated=True, lam=1.0, callback=None, **kwargs)[source]

Calls odl.solvers.nonsmooth.proximal_gradient_solvers.proximal_gradient or odl.solvers.nonsmooth.proximal_gradient_solvers .accelerated_proximal_gradient.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • gamma (positive float, optional) – Step size parameter (default 0.001).

  • reg ([type of ] odl.solvers.functional.Functional, optional) – The regularization functional of the inverse problem. Needs to have f.proximal. If a type is passed instead, the functional is constructed by calling reg(op.domain). Default: odl.solvers.L1Norm.

  • accelerated (boolean, optional) – Indicates which algorithm to use. If False, then the “Iterative Soft-Thresholding Algorithm” (ISTA) is used. If True, then the accelerated version FISTA is used. Default: True.

  • lam (float or callable, optional) – Overrelaxation step size (default 1.0). If callable, it should take an index (starting at zero) and return the corresponding step size.

  • callback (odl.solvers.util.callback.Callback, optional) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.PDHGReconstructor(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Primal-Dual Hybrid Gradient (PDHG) algorithm from the 2011 paper https://link.springer.com/article/10.1007/s10851-010-0251-1 with TV regularization.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

lam

TV-regularization rate (default 0.01).

Type:

positive float, optional

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Calls odl.solvers.nonsmooth.primal_dual_hybrid_gradient.pdhg.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • lam (positive float, optional) – TV-regularization rate (default 0.01).

  • callback (odl.solvers.util.callback.Callback or None) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.DouglasRachfordReconstructor(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Douglas-Rachford primal-dual splitting algorithm from the 2012 paper https://arxiv.org/abs/1212.0326 with TV regularization.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

lam

TV-regularization rate (default 0.01).

Type:

positive float, optional

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Calls odl.solvers.nonsmooth.douglas_rachford.douglas_rachford_pd.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • lam (positive float, optional) – TV-regularization rate (default 0.01).

  • callback (odl.solvers.util.callback.Callback or None) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.ForwardBackwardReconstructor(op, x0, niter=None, lam=0.01, tau=0.01, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

The forward-backward primal-dual splitting algorithm.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

lam

TV-regularization rate (default 0.01).

Type:

positive float, optional

tau

Step-size like parameter for f (default is 0.01).

Type:

positive float, optional

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, lam=0.01, tau=0.01, callback=None, **kwargs)[source]

Calls odl.solvers.forward_backward_pd.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • lam (positive float, optional) – TV-regularization rate (default 0.01).

  • tau (positive float, optional) – Step-size like parameter for f (default is 0.01).

  • callback (odl.solvers.util.callback.Callback or None) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.ADMMReconstructor(op, x0, niter=None, lam=0.01, tau=0.01, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Generic linearized ADMM method for convex problems. ADMM stands for ‘Alternating Direction Method of Multipliers’.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

lam

TV-regularization weight (default 0.01).

Type:

positive float, optional

tau

Step-size like parameter for f (default is 0.01).

Type:

positive float, optional

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, lam=0.01, tau=0.01, callback=None, **kwargs)[source]

Calls odl.solvers.nonsmooth.admm.admm_linearized.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • lam (positive float, optional) – TV-regularization weight (default 0.01).

  • tau (positive float, optional) – Step-size like parameter for f (default is 0.01).

  • callback (odl.solvers.util.callback.Callback or None) – Object that is called in each iteration.

property iterations
class dival.reconstructors.odl_reconstructors.BFGSReconstructor(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Bases: _IterativeODLReconstructor

Quasi-Newton BFGS method to minimize a differentiable function. The TV regularization term is smoothed using the Moreau envelope.

op

The forward operator of the inverse problem.

Type:

odl.operator.Operator

x0

Initial value.

Type:

op.domain element

niter

Number of iterations.

Type:

int

lam

TV-regularization weight (default 0.01).

Type:

positive float, optional

callback

Object that is called in each iteration.

Type:

odl.solvers.util.callback.Callback or None

__init__(op, x0, niter=None, lam=0.01, callback=None, **kwargs)[source]

Calls odl.solvers.smooth.newton.bfgs_method.

Parameters:

  • op (odl.operator.Operator) – The forward operator of the inverse problem.

  • x0 (op.domain element) – Initial value.

  • niter (int) – Number of iterations (overriding self.hyper_params["iterations"] initially).

  • lam (positive float, optional) – TV-regularization weight (default 0.01).

  • callback (odl.solvers.util.callback.Callback or None) – Object that is called in each iteration.

property iterations