tfmri.signal.nufft

nufft(source, points, grid_shape=None, transform_type='type_2', fft_direction='forward', tol=1e-06, options=None)

Computes the non-uniform discrete Fourier transform via NUFFT.

Evaluates the type-1 or type-2 non-uniform discrete Fourier transform (NUDFT) via the non-uniform fast Fourier transform (NUFFT) algorithm. Supports 1D, 2D and 3D transforms.

````{warning} Currently 1D transforms are only supported on the CPU. ````

Parameters

  • source – A tf.Tensor of type complex64 or complex128. The source grid, for type-2 transforms, or the source point set, for type-1 transforms. If transform_type is "type_2", source must have shape [...] + grid_shape, where grid_shape is the shape of the grid and ... is any number of batch dimensions. grid_shape must have rank 1, 2 or 3. If transform_type is "type_1", source must have shape [..., M], where M is the number of non-uniform points and ... is any number of batch dimensions.

  • points –

    A tf.Tensor of type float32 or float64. float64. The target non-uniform point coordinates, for type-2 transforms, or the source non-uniform point coordinates, for type-1 transforms. Must have shape [..., M, N], where M is the number of non-uniform points, N is the rank of the grid and ... is any number of batch dimensions, which must be broadcastable with the batch dimensions of source. N must be 1, 2 or 3 and must be equal to the rank of grid_shape. The non-uniform coordinates must be in units of radians/pixel, i.e., in the range [-pi, pi].

  • grid_shape –

    A 1D tf.Tensor of type int32 or int64. The shape of the output grid. This argument is required for type-1 transforms and ignored for type-2 transforms.

  • transform_type – An optional str from "type_1", "type_2". The type of the transform. A "type_2" transform evaluates the DFT on a set of arbitrary points given points on a grid (uniform to non-uniform). A "type_1" transform evaluates the DFT on grid points given a set of arbitrary points (non-uniform to uniform).

  • fft_direction –

    An optional str from "forward", "backward". Defines the sign of the exponent in the formula of the Fourier transform. A "forward" transform has negative sign and a "backward" transform has positive sign.

  • tol – An optional float. The desired relative precision. Should be in the range [1e-06, 1e-01] for complex64 types and [1e-14, 1e-01] for complex128 types. The computation may take longer for smaller values of tol. Defaults to 1e-06.

  • options – A tfft.Options structure specifying advanced options. These options may affect the internal details of the computation, but do not change the result (beyond the precision specified by tol). You might be able to optimize performance or memory usage by tweaking these options. See tfft.Options for details.

Returns

A tf.Tensor of the same type as source. The target point set, for type-2 transforms, or the target grid, for type-1 transforms. If transform_type is "type_2", the output has shape [..., M], where the batch shape ... is the result of broadcasting the batch shapes of source and points. If transform_type is "type_1", the output has shape [...] + grid_shape, where the batch shape ... is the result of broadcasting the batch shapes of source and points.

References

  1. Barnett, A.H., Magland, J. and Klinteberg, L. af (2019), A parallel nonuniform fast Fourier transform library based on an “exponential of semicircle” kernel. SIAM J. Sci. Comput., 41(5): C479-C504. https://doi.org/10.1137/18M120885X

  2. Shih Y., Wright G., Anden J., Blaschke J. and Barnett A.H. (2021), cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs. 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), 688-697 https://doi.org/10.1109/IPDPSW52791.2021.00105