linop.wave_calibrate

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linop.wave_calibrate#

bartorch.linop.wave_calibrate()#

Fit the wave’s gradient amplitude and delay to a wave-free calibration region.

The model predicts the wave-encoded samples from the reference: inverse FFT along the phase encodes, multiplication by wave_psf(), and FFT back. Per phase-encode axis, scale and delay are fitted by nonlinear least squares (scipy.optimize.least_squares) starting from 1 and 0. The residual is taken on the acquired wave lines whose neighbourhood, within the wave’s largest excursion in lines, lies inside the calibration region; k-space outside the region is neglected.

Parameters:

  • reference (array_like) – Wave-free k-space (coils, [kz,] ky, readout), zero outside the calibration region, with the readout in acquisition order.

  • wave (array_like) – Wave-encoded k-space on the same grid, zero where not acquired.

  • trajectory (array_like) – Nominal wave trajectory, as for wave_psf().

  • fov (float or tuple of float) – Field of view along the phase encodes in m, one value or (z, y).

Returns:

scale, delay – One per phase encode, (z, y) in 3D: the gradient amplitude relative to nominal and the delay in readout samples, as wave_psf() takes them.

Return type:

tuple of float

Raises:

ValueError – When the shapes disagree, or no acquired line has its neighbourhood inside the calibration region.

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