compute_svd_coefficients

compute_svd_coefficients#

mrinufft.extras.field_map.compute_svd_coefficients(field_map, readout_time, mask, L=-1, n_bins=1024, lazy=False, partial_svd=True)[source]#

Compute off-resonance correction coefficients using an SVD.

Solves \(\arg\min_{B,C} = \|E - BC \|_{F}^2\)

In practise it utilizes truncated SVD to extract L leading singular vectors from the weighted exponentiated phase matrix sampled at field map histogram centers.

Parameters:

  • field_map (NDArray) – The field map (off-resonance map) in rad/s, If complex-valued, the real part is interpreted as R2* mapping. If real-valued this is the field inhomogeneities in Hz. and will be multiplied by \(2j\pi\)

  • readout_time (NDArray) – The vector of time points (in seconds) at which to compute phase evolution.

  • mask (NDArray) – Binary mask indicating object region for field map/statistics.

  • L (int, optional) – Number of virtual centers or basis functions retained (default is -1, automatically estimated).

  • n_bins (int, optional) – Number of histogram bins for off-resonance value clustering (default is 1000).

  • lazy (bool, default False) – If True, use a lazy evaluation scheme for the space interpolator C, saving memory.

  • partial_svd (bool, default True) – If True, only compute the L components required for the estimation, not the full SVD.

Returns:

  • B (NDArray) – [L, nbins] phase basis matrix in the time domain.

  • C (NDArray) – [L, nt] interpolation matrix to transform weighted basis to phase at the time points; nt = len(readout_time).

  • E (NDArray) – [nbins, nt] exponential off-resonance phase matrix at input histogram bins.

References

Sutton BP, Noll DC, Fessler JA. Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities. IEEE Trans Med Imaging. 2003 Feb;22(2):178-88. doi: 10.1109/tmi.2002.808360. PMID: 12715994.

Note

This function uses numpy for all CPU arrays, and cupy for all on-gpu array. It will convert all its array argument to the respective array library. The outputs will be converted back to the original array module and device.

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