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deepmr.fermi

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deepmr.fermi#

deepmr.fermi(ndim, size, width=None)[source]#

Build a n-dimensional Fermi filter.

This routine can handle isotropic ND matrices. User can specify the size of window support and the FWHM. The filter can be used in the context of image processing to mitigate ringing artifact [1].

Parameters:

  • ndim (int) – Number of dimensions (e.g., 1=1D, 2=2D, 3=3D).

  • size (int) – Support of the window. Filter size will be ndim * [size].

  • width (int, optional) – Full width half maximum of the filter. If None, it is automatically set to size. The default is None.

Returns:

filt – Fermi window of shape ndim * [size] and FWHM = width.

Return type:

torch.Tensor

Example

>>> import deepmr

We can design e.g., 1D, 2D or 3D filters as:

>>> filt1d = deepmr.fermi(1, 128)
>>> filt1d.shape
torch.Size([128])
>>> filt2d = deepmr.fermi(2, 128)
torch.Size([128, 128])
>>> filt3d = deepmr.fermi(3, 128)
torch.Size([128, 128])

Bu default, FWHM is equal to the support size:

>>> (filt1d >= 0.5).sum()
tensor(128)

User can specify a smaller FWHM via width parameter:

>>> filt1d = deepmr.fermi(1, 128, width=32)
>>> filt1d.shape
torch.Size([128])
>>> (filt1d >= 0.5).sum()
tensor(47)

The discrepancy between nominal and actual FWHM is due to signal discretization.

References

[1] Bernstein, M.A., Fain, S.B. and Riederer, S.J. (2001), Effect of windowing and zero-filled reconstruction of MRI data on spatial resolution and acquisition strategy. J. Magn. Reson. Imaging, 14: 270-280. https://doi.org/10.1002/jmri.1183

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