UFT¶
Undersampled Fourier transform encoding model.
I’m calling “encoding model” how we encode the image domain signal to get to the acquisiton domain. In the case of MR, we measure k-space of the image we want, so the encoding model is simply the Fourier transform (ignoring all the other complications…). This object provides methods to go into k-space and get back out assuming we undersample according to some mask.
forward_ortho, inverse_ortho are probably the ones you want.
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class
mr_utils.cs.models.UFT.UFT(samp, axes=None, scale=True)[source]¶ Undersampled Fourier Transform (UFT) data acquisiton model.
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samp¶ Boolean sampling pattern.
Type: array_like
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axes¶ Axes to perform FFT over.
Type: tuple
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scale¶ Whether or not to scale ortho transforms.
Type: bool
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forward(x, axes=None)[source]¶ Fourier encoding with binary undersampling pattern applied.
Parameters: - x (array_like) – Matrix to be transformed.
- axes (tuple) – Dimensions to Fourier transform if x is not 2d.
Returns: Fourier transform (no fftshift) of x with sampling mask applied.
Return type: array_like
Notes
This forward transform has no fftshift applied.
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forward_ortho(x, axes=None)[source]¶ Normalized Fourier encoding with binary undersampling.
Parameters: - x (array_like) – Matrix to be transformed.
- axes (tuple, optional) – Dimensions to perform FFT2 over.
Returns: Fourier transform of x with sampling mask applied and normalized.
Return type: array_like
Notes
This forward transform applied fftshift before FFT and after.
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forward_s(x)[source]¶ Fourier encoding with binary undersampling pattern applied.
Parameters: x (array_like) – Matrix to be transformed. Returns: Fourier transform (with fftshift) of x with sampling mask applied. Return type: array_like Notes
This forward transform applies fftshift before masking.
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inverse(x, axes=None)[source]¶ Inverse fourier encoding.
Parameters: - x (array_like) – Matrix to be transformed.
- axes (tuple) – Dimensions to Fourier transform if x is not 2d.
Returns: Inverse fourier transform of x.
Return type: array_like
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inverse_ortho(x, axes=None)[source]¶ Inverse Normalized Fourier encoding.
Parameters: - x (array_like) – Matrix to be transformed.
- axes (tuple, optional) – Dimensions to Fourier transform if x is not 2d.
Returns: Inverse fourier transform of x, fftshifted, and normalized.
Return type: array_like
Notes
This transform applied ifftshift before and after ifft2.
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