mri.operators.fourier.utils.orc_coefficients

Functions to compute different kinds of coefficients used in Off-Resonance Correction.

compute_orc_coefficients(field_map, time_vec, mask, coefficients='svd', num_interpolators=15, weights='full', n_bins=1000)

This function computes different off-resonance correction weights used in the ORCFFTWrapper, as described in: - :cite: man1997 for Multi-Frequency Interpolation (MFI) - :cite: sutton2003 for Multi-Temporal Interpolation (MTI) - :cite: fessler2005 for (Fast) Singular Value Decomposition (SVD, FSVD)

Parameters

• field_map (numpy.ndarray) – B0 field inhomogeneity map (in Hz)

• time_vec (numpy.ndarray) – 1D vector indicating time after pulse in each shot (in s)

• mask (numpy.ndarray) – Mask describing the regions to consider during correction

• coefficients ({'mfi', 'mti', 'svd', 'fsvd'}) – Computation method used to obtain the interpolation weights.

• L (int) – Number of interpolators used for multi-linear correction (default 15)

• weights ({'full', 'sqrt', 'log', 'ones'}) – Weightning policy for the field map histogram (default ‘full’)

• n_bins (int) – Number of bins for the field map histogram (default 1000)

Returns

• B (numpy.ndarray) – (len(time_vec), L) array correspondig to k-space coefficients

• C (numpy.ndarray) – (L, n_bins) array corresponding to volume coefficients

• E (numpy.ndarray) – (len(time_vec), n_bins) array corresponding to the target matrix

_create_histogram(field_map, mask, weights='full', n_bins=1000)

Create the weighted histogram of the field map covered by the mask

Parameters

• field_map (numpy.ndarray) – B0 field inhomogeneity map (in Hz)

• mask (numpy.ndarray) – Mask describing the regions to consider during correction

• weights ({'full', 'sqrt', 'log', 'ones'}) – Weightning policy for the field map histogram (default ‘full’)

• n_bins (int) – Number of bins for the field map histogram (default 1000)

Returns

• histogram_centers (numpy.ndarray) – Central values of each bin

• histogram_counts (numpy.ndarray) – Weights of elements in each bin according to args

_create_variable_density(centers, counts, L)

Find a reduced histogram with variable density from previous histogram

Parameters

• centers (numpy.ndarray) – Central value of each bin from previous histogram

• counts (numpy.ndarray) – Number of elements in each bin from previous histogram

• L (int) – Number of interpolators defining the size of the reduced histogram

Returns

centers – New bin centers of the reduced histogram

Return type

numpy.ndarray

_compute_mfi_coefficients(field_map, time_vec, mask, L=15, weights='full', n_bins=1000)

_compute_mti_coefficients(field_map, time_vec, mask, L=15, weights='full', n_bins=1000)

_compute_svd_coefficients(field_map, time_vec, mask, L=15, weights='full', n_bins=1000)

_compute_fsvd_coefficients(field_map, time_vec, mask, L=15, weights='full', n_bins=1000)