mri.operators.proximity#

class AutoWeightedSparseThreshold(coeffs_shape, linear=<modopt.opt.linear.base.Identity object>, update_period=0, sigma_range='global', thresh_range='global', threshold_estimation='sure', threshold_scaler=1.0, **kwargs)[source]#

Bases: modopt.opt.proximity.SparseThreshold

Automatic Weighting of sparse coefficients.

This proximty automatically determines the threshold for Sparse (e.g. Wavelet based) coefficients.

The weight are computed on first call, and updated on every update_period call. Note that the coarse/approximation scale will not be thresholded.

Parameters

  • coeffs_shape (list of tuple) – list of shape for the subbands.

  • linear (LinearOperator) – Required for cost estimation.

  • update_period (int) – Estimation of the weight update period.

  • threshold_estimation (str) – threshold estimation method. Available are “sure”, “hybrid-sure” and “universal”

  • thresh_range (str) – threshold range of estimation. Available are “global”, “scale” and “band”

  • sigma_range (str) – noise std range of estimation. Available are “global”, “scale” and “band”

  • thresh_type (str) – “hard” or “soft” thresholding.

_auto_thresh(input_data)[source]#

Compute the best weights for the input_data.

Parameters

input_data (numpy.ndarray) – Array of sparse coefficient.

See also

wavelet_threshold_estimate

_op_method(input_data, extra_factor=1.0)[source]#

Operator.

This method returns the input data thresholded by the weights. The weights are computed using the universal threshold rule.

Parameters

  • input_data (numpy.ndarray) – Input data array

  • extra_factor (float) – Additional multiplication factor (default is 1.0)

Returns

Thresholded data

Return type

numpy.ndarray

class WeightedSparseThreshold(weights, coeffs_shape, weight_type='scale_based', zero_weight_coarse=True, linear=<modopt.opt.linear.base.Identity object>, **kwargs)[source]#

Bases: modopt.opt.proximity.SparseThreshold

This is a weighted version of SparseThreshold in ModOpt. When chosen scale_based, it allows the users to specify an array of weights W[i] and each weight is assigen to respective scale i. Also, custom weights can be defined. Note that the weights on coarse scale is always set to 0

Parameters

  • weights (numpy.ndarray) – Input array of weights or a tuple holding base weight W and power P

  • coeffs_shape (tuple) – The shape of linear coefficients

  • weight_type (string 'custom' | 'scale_based' | 'custom_scale',) – default ‘scale_based’ Mode of operation of proximity: custom -> custom array of weights scale_based -> custom weights applied per scale

  • zero_weight_coarse (bool, default True) –

  • linear (object, default Identity()) – Linear operator, to be used in cost function evaluation

See also

SparseThreshold

parent class

property mu#

mu is the weights used for thresholding

class OWL(alpha, beta, bands_shape, n_coils, mode='band_based', n_jobs=1)[source]#

Bases: modopt.opt.proximity.ProximityParent

This class handles reshaping coefficients based on mode and feeding in right format the OWL operation to OrderedWeightedL1Norm

Parameters

  • alpha (float) – value of alpha for parameterizing weights

  • beta (float) – value of beta for parameterizing weights

  • band_shape (list of tuples) – the shape of all bands, this corresponds to linear_op.coeffs_shape

  • n_coils (int) – number of channels

  • mode (string 'all' | 'band_based' | 'coeff_based' | 'scale_based',) – default ‘band_based’ Mode of operation of proximity: all -> on all coefficients in all channels band_based -> on all coefficients in each band coeff_based -> on all coefficients but across each channel scale_based -> on al coefficients in each scale

  • n_jobs (int, default 1) – number of cores to be used for operation

static _oscar_weights(alpha, beta, size)[source]#

Here we parametrize weights based on alpha and beta

_reshape_band_based(data)[source]#

Function to reshape incoming data based on bands

_reshape_scale_based(data)[source]#
_op_method(data, extra_factor=1.0)[source]#

Based on mode, reshape the coefficients and call OrderedWeightedL1Norm

Parameters

data (numpy.ndarray) – Input array of data

_cost_method(data)[source]#

Cost function Based on mode, reshape the incoming data and call cost in OrderedWeightedL1Norm This method calculate the cost function of the proximable part.

Parameters

data (numpy.ndarray) – Input array of the sparse code.

Returns

Return type

The cost of this sparse code

Submodules#