ppftpy.rppft2#

ppftpy.rppft2(data, /, *, vectorized=False, scipy_fft=False)[source]#

Compute the 2D Pseudo-Polar Fourier Transform for real input.

This function computes the 2-dimensional Pseudo-Polar Fourier Transform [Averbuch2001] for real input. The real PPFT2D computes only the non-redundant half of the spectrum.

Parameters:

  • data (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – The input data, either a single 2D matrix (shape (N, N)) or a batch of 2D matrices (shape (V, N, N)). Each matrix must be square with even length. The data can be either real or complex.

  • scipy_fft (bool) – If True, uses SciPy’s FFT backend (scipy.fft) or a registered backend via SciPy’s backend control instead of the native array’s FFT implementation (e.g., numpy.fft). This may improve performance but requires SciPy to be installed.

  • vectorized (bool) – If True, computes the transform using a fully vectorized approach. This is significantly faster but requires more memory. Use with caution for large datasets.

Return type:

ndarray[tuple[Any, ...], dtype[complex128 | clongdouble]]

Returns:

The computed 2D Pseudo-Polar Fourier Transform. The output shape depends on the input:

  • If data has shape (N, N), the output has shape (2, N+1, N+1).

  • If data has shape (V, N, N), the output has shape (V, 2, N+1, N+1).

Raises:

  • ValueError – If the input shape is not (N, N) (single 2D matrix) or (V, N, N) (multiple 2D matrices) with even N and arbitrary V.

  • ModuleNotFoundError – If scipy_fft=True but SciPy is not installed.

  • TypeError – If the input data is complex.

See also

ppft2

The 2D Pseudo-Polar Fourier Transform.

rppft3

The 3D Pseudo-Polar Fourier Transform of real input.

References

[Averbuch2001]

A. Averbuch, R. Coifman, D. Donoho, M. Israeli, and J. Waldén, “Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computible, Algebraically Exact, Geometrically Faithful and Invertible,” 2001.

Examples

>>> from ppftpy import rppft2
>>> import numpy as np
>>> arr = np.random.default_rng().random((4, 4))
>>> rppft2(arr).shape
(2, 5, 5)

Compute PPFT2D for 3 arrays.

>>> from ppftpy import rppft2
>>> import numpy as np
>>> arr = np.random.default_rng().random((3, 4, 4))
>>> rppft2(arr).shape
(3, 2, 5, 5)
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