tools.field_map_from_phase

bartorch.tools.field_map_from_phase()

Off-resonance frequency from the phase of single-echo coil images.

Coil sensitivities \(s_c\) are the coil images low-pass filtered to calibration_width of k-space. The images are combined as \(m = \sum_c x_c s_c^* / \sum_c |s_c|^2\), which removes the coil and object phase varying as slowly as the sensitivities, the complex result is Gaussian-smoothed, and the field is \(f = \arg(m) / (2\pi\, \mathrm{TE})\). It is unambiguous for \(|f| < 1 / (2\,\mathrm{TE})\) and includes the chemical shift of fat.

Parameters:

• coil_images (torch.Tensor) – Complex uncombined images (coils, z, y, x).

• echo_time (float) – Echo time, in seconds.

• smoothing (float, default=2.0) – Standard deviation of the Gaussian applied to the combined image, in voxels.

• calibration_width (float, default=0.06) – Half-width of the Hann taper that low-pass filters the coil images into sensitivities, as a fraction of each k-space axis’s Nyquist extent.

Returns:

Off-resonance frequency in Hz, real, of shape (z, y, x).

Return type:

torch.Tensor

Raises:

ValueError – If the images are not complex or not (coils, z, y, x), or echo_time is not positive.