"""
Implements class BandPassFilter to create Fourier filter representations.
Copyright (c) 2024 European Molecular Biology Laboratory
Author: Valentin Maurer <valentin.maurer@embl-hamburg.de>
"""
from typing import Tuple, Dict
import numpy as np
from scipy.ndimage import mean as ndimean
from scipy.ndimage import map_coordinates
from ..types import BackendArray
from ..backends import backend as be
from .compose import ComposableFilter
from ._utils import fftfreqn, compute_fourier_shape, shift_fourier
__all__ = ["LinearWhiteningFilter"]
[docs]
class LinearWhiteningFilter(ComposableFilter):
"""
Compute Fourier power spectrums and perform whitening.
Parameters
----------
**kwargs : Dict, optional
Additional keyword arguments.
References
----------
.. [1] de Teresa-Trueba, I.; Goetz, S. K.; Mattausch, A.; Stojanovska, F.; Zimmerli, C. E.;
Toro-Nahuelpan, M.; Cheng, D. W. C.; Tollervey, F.; Pape, C.; Beck, M.; Diz-Munoz,
A.; Kreshuk, A.; Mahamid, J.; Zaugg, J. B. Nat. Methods 2023, 20, 284–294.
.. [2] M. L. Chaillet, G. van der Schot, I. Gubins, S. Roet,
R. C. Veltkamp, and F. Förster, Int. J. Mol. Sci. 24,
13375 (2023)
"""
def __init__(self, **kwargs):
pass
@staticmethod
def _compute_spectrum(
data_rfft: BackendArray, n_bins: int = None, batch_dimension: int = None
) -> Tuple[BackendArray, BackendArray]:
"""
Compute the power spectrum of the input data.
Parameters
----------
data_rfft : BackendArray
The Fourier transform of the input data.
n_bins : int, optional
The number of bins for computing the spectrum, defaults to None.
batch_dimension : int, optional
Batch dimension to average over.
Returns
-------
bins : BackendArray
Array containing the bin indices for the spectrum.
radial_averages : BackendArray
Array containing the radial averages of the spectrum.
"""
shape = tuple(x for i, x in enumerate(data_rfft.shape) if i != batch_dimension)
max_bins = max(max(shape[:-1]) // 2 + 1, shape[-1])
n_bins = max_bins if n_bins is None else n_bins
n_bins = int(min(n_bins, max_bins))
bins = fftfreqn(
shape=shape,
sampling_rate=0.5,
shape_is_real_fourier=True,
compute_euclidean_norm=True,
)
bins = be.to_numpy_array(bins)
# Implicit lowpass to nyquist
bins = np.floor(bins * (n_bins - 1) + 0.5).astype(int)
fft_shift_axes = tuple(
i for i in range(data_rfft.ndim - 1) if i != batch_dimension
)
fourier_spectrum = np.fft.fftshift(data_rfft, axes=fft_shift_axes)
fourier_spectrum = np.abs(fourier_spectrum)
np.square(fourier_spectrum, out=fourier_spectrum)
radial_averages = ndimean(
fourier_spectrum, labels=bins, index=np.arange(n_bins)
)
np.sqrt(radial_averages, out=radial_averages)
np.reciprocal(radial_averages, out=radial_averages)
np.divide(radial_averages, radial_averages.max(), out=radial_averages)
return bins, radial_averages
@staticmethod
def _interpolate_spectrum(
spectrum: BackendArray,
shape: Tuple[int],
shape_is_real_fourier: bool = True,
order: int = 1,
) -> BackendArray:
grid = fftfreqn(
shape=shape,
sampling_rate=0.5,
shape_is_real_fourier=shape_is_real_fourier,
compute_euclidean_norm=True,
)
grid = be.to_numpy_array(grid)
np.multiply(grid, (spectrum.shape[0] - 1), out=grid) + 0.5
spectrum = map_coordinates(spectrum, grid.reshape(1, -1), order=order)
return spectrum.reshape(grid.shape)
[docs]
def __call__(
self,
shape: Tuple[int],
data: BackendArray = None,
data_rfft: BackendArray = None,
n_bins: int = None,
batch_dimension: int = None,
order: int = 1,
return_real_fourier: bool = True,
**kwargs: Dict,
) -> Dict:
"""
Apply linear whitening to the data and return the result.
Parameters
----------
shape : tuple of ints
Shape of the returned whitening filter.
data : BackendArray, optional
The input data, defaults to None.
data_rfft : BackendArray, optional
The Fourier transform of the input data, defaults to None.
n_bins : int, optional
The number of bins for computing the spectrum, defaults to None.
batch_dimension : int, optional
Batch dimension to average over.
return_real_fourier : tuple of int
Return a shape compliant with rfft, i.e., omit the negative frequencies
terms resulting in a return shape (*shape[:-1], shape[-1]//2+1)
**kwargs : Dict
Additional keyword arguments.
Returns
-------
dict
data: BackendArray
The filter mask.
shape: tuple of ints
The requested filter shape
return_real_fourier: bool
Whether data is compliant with rfftn.
is_multiplicative_filter: bool
Whether the filter is multiplicative in Fourier space.
"""
if data_rfft is None:
data_rfft = be.rfftn(data)
data_rfft = be.to_numpy_array(data_rfft)
bins, radial_averages = self._compute_spectrum(
data_rfft, n_bins, batch_dimension
)
shape = tuple(int(x) for i, x in enumerate(shape) if i != batch_dimension)
shape_filter = shape
if return_real_fourier:
shape_filter = compute_fourier_shape(
shape=shape,
shape_is_real_fourier=False,
)
ret = self._interpolate_spectrum(
spectrum=radial_averages,
shape=shape_filter,
shape_is_real_fourier=return_real_fourier,
)
ret = shift_fourier(data=ret, shape_is_real_fourier=return_real_fourier)
return {
"data": be.to_backend_array(ret),
"shape": shape,
"return_real_fourier": return_real_fourier,
"is_multiplicative_filter": True,
}