"""SMaps module for sensitivity maps estimation."""
from __future__ import annotations
from mrinufft.density.utils import flat_traj
from mrinufft._utils import get_array_module
from mrinufft._array_compat import with_numpy_cupy
from .utils import register_smaps
import numpy as np
from numpy.typing import NDArray
from collections.abc import Callable
def _extract_kspace_center(
kspace_data: NDArray,
kspace_loc: NDArray,
threshold: float | tuple[float, ...] = None,
density: NDArray | None = None,
window_fun: str | Callable[[NDArray], NDArray] = "ellipse",
) -> tuple[NDArray, NDArray, NDArray | None]:
r"""Extract k-space center and corresponding sampling locations.
The extracted center of the k-space, i.e. both the kspace locations and
kspace values. If the density compensators are passed, the corresponding
compensators for the center of k-space data will also be returned. The
return dtypes for density compensation and kspace data is same as input
Parameters
----------
kspace_data: numpy.ndarray
The value of the samples
kspace_loc: numpy.ndarray
The samples location in the k-space domain (between [-0.5, 0.5[)
threshold: tuple or float
The threshold used to extract the k_space center (between (0, 1])
window_fun: "Hann", "Hanning", "Hamming", or a callable, default None.
The window function to apply to the selected data. It is computed with
the center locations selected. Only works with circular mask.
If window_fun is a callable, it takes as input the array (n_samples x n_dims)
of sample positions and returns an array of n_samples weights to be
applied to the selected k-space values, before the smaps estimation.
Returns
-------
data_thresholded: ndarray
The k-space values in the center region.
center_loc: ndarray
The locations in the center region.
density_comp: ndarray, optional
The density compensation weights (if requested)
Notes
-----
The Hann (or Hanning) and Hamming windows of width :math:`2\theta` are defined as:
.. math::
w(x,y) = a_0 - (1-a_0) * \cos(\pi * \sqrt{x^2+y^2}/\theta),
\sqrt{x^2+y^2} \le \theta
In the case of Hann window :math:`a_0=0.5`.
For Hamming window we consider the optimal value in the equiripple sense:
:math:`a_0=0.53836`.
.. Wikipedia:: https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows
"""
xp = get_array_module(kspace_data)
if isinstance(threshold, float):
threshold = (threshold,) * kspace_loc.shape[1]
if window_fun == "rect":
data_ordered = xp.copy(kspace_data)
index = xp.linspace(
0, kspace_loc.shape[0] - 1, kspace_loc.shape[0], dtype=xp.int64
)
condition = xp.logical_and.reduce(
tuple(
xp.abs(kspace_loc[:, i]) <= threshold[i] for i in range(len(threshold))
)
)
index = xp.extract(condition, index)
center_locations = kspace_loc[index, :]
data_thresholded = data_ordered[:, index]
dc = density[index]
return data_thresholded, center_locations, dc
else:
if callable(window_fun):
window = window_fun(kspace_loc)
else:
if window_fun in ["hann", "hanning", "hamming"]:
radius = xp.linalg.norm(kspace_loc, axis=1)
a_0 = 0.5 if window_fun in ["hann", "hanning"] else 0.53836
window = a_0 + (1 - a_0) * xp.cos(xp.pi * radius / threshold)
elif window_fun == "ellipse":
window = xp.sum(kspace_loc**2 / xp.asarray(threshold) ** 2, axis=1) <= 1
else:
raise ValueError("Unsupported window function.")
data_thresholded = window * kspace_data
# Return k-space locations & density just for consistency
return data_thresholded, kspace_loc, density
[docs]
@register_smaps
@flat_traj
def low_frequency(
traj: NDArray,
shape: tuple[int, ...],
kspace_data: NDArray,
backend: str,
threshold: float | tuple[float, ...] = 0.1,
density: NDArray | None = None,
window_fun: str | Callable[[NDArray], NDArray] = "ellipse",
blurr_factor: int | float | tuple[float, ...] = 0.0,
mask: bool = False,
) -> tuple[NDArray, NDArray]:
"""
Calculate low-frequency sensitivity maps.
Parameters
----------
traj : numpy.ndarray
The trajectory of the samples.
shape : tuple
The shape of the image.
kspace_data : numpy.ndarray
The k-space data.
threshold : float, or tuple of float, optional
The threshold used for extracting the k-space center.
By default it is 0.1
backend : str
The backend used for the operator.
density : numpy.ndarray, optional
The density compensation weights.
window_fun: "Hann", "Hanning", "Hamming", or a callable, default None.
The window function to apply to the selected data. It is computed with
the center locations selected. Only works with circular mask.
If window_fun is a callable, it takes as input the array (n_samples x n_dims)
of sample positions and returns an array of n_samples weights to be
applied to the selected k-space values, before the smaps estimation.
blurr_factor : float or list, optional
The blurring factor for smoothing the sensitivity maps.
Applies a gaussian filter on the Smap images to get smoother Sensitivty maps.
By default it is 0.0, i.e. no smoothing is done
mask: bool, optional default `False`
Whether the Sensitivity maps must be masked
Returns
-------
Smaps : numpy.ndarray
The low-frequency sensitivity maps.
SOS : numpy.ndarray
The sum of squares of the sensitivity maps.
"""
# defer import to later to prevent circular import
from mrinufft import get_operator
try:
from skimage.filters import threshold_otsu, gaussian
from skimage.morphology import convex_hull_image
except ImportError as err:
raise ImportError(
"The scikit-image module is not available. Please install "
"it along with the [extra] dependencies "
"or using `pip install scikit-image`."
) from err
k_space, samples, dc = _extract_kspace_center(
kspace_data=kspace_data,
kspace_loc=traj,
threshold=threshold,
density=density,
window_fun=window_fun,
)
smaps_adj_op = get_operator(backend)(
samples, shape, density=dc, n_coils=k_space.shape[-2]
)
Smaps = smaps_adj_op.adj_op(k_space)
SOS = np.linalg.norm(Smaps, axis=0)
if mask:
thresh = threshold_otsu(SOS)
# Create convex hull from mask
convex_hull = convex_hull_image(SOS > thresh)
Smaps = Smaps * convex_hull
# Smooth out the sensitivity maps
if np.sum(blurr_factor) > 0:
if isinstance(blurr_factor, (float, int)):
blurr_factor = (blurr_factor,) * SOS.ndim
Smaps = gaussian(np.abs(Smaps), sigma=(0,) + blurr_factor) * np.exp(
1j * np.angle(Smaps)
)
# Re-normalize the sensitivity maps
if mask or np.sum(blurr_factor) > 0:
# ReCalculate SOS with a minor eps to ensure divide by 0 is ok
SOS = np.linalg.norm(Smaps, axis=0) + 1e-10
Smaps = Smaps / SOS
return Smaps, SOS
[docs]
@with_numpy_cupy
def coil_compression(
kspace_data: NDArray,
K: int | float,
traj: NDArray | None = None,
krad_thresh: float | None = None,
) -> NDArray:
"""
Coil compression using principal component analysis on k-space data.
Parameters
----------
kspace_data : NDArray
Multi-coil k-space data. Shape: (n_coils, n_samples).
K : int or float
Number of virtual coils to retain (if int), or energy threshold (if
float between 0 and 1).
traj : NDArray, optional
Sampling trajectory. Shape: (n_samples, n_dims).
krad_thresh : float, optional
Relative k-space radius (as a fraction of maximum) to use for selecting
the calibration region for principal component analysis. If None, use
all k-space samples.
Returns
-------
NDArray
Coil-compressed data. Shape: (K, n_samples) if K is int, number of
retained components otherwise.
"""
xp = get_array_module(kspace_data)
if krad_thresh is not None and traj is not None:
traj_rad = xp.sqrt(xp.sum(traj**2, axis=-1))
center_data = kspace_data[:, traj_rad < krad_thresh * xp.max(traj)]
elif krad_thresh is None:
center_data = kspace_data
else:
raise ValueError("traj and krad_thresh must be specified.")
# Compute the covar matrix of selected data
cov = center_data @ center_data.T.conj()
w, v = xp.linalg.eigh(cov)
# sort eigenvalues largest to smallest
si = xp.argsort(w)[::-1]
w_sorted = w[si]
v_sorted = v[si]
if isinstance(K, float):
# retain enough components to reach energy K
w_cumsum = xp.cumsum(w_sorted) # from largest to smallest
total_energy = xp.sum(w_sorted)
K = int(xp.searchsorted(w_cumsum / total_energy, K, side="left") + 1)
K = min(K, w_sorted.size)
V = v_sorted[:K] # use top K component
compress_data = V @ kspace_data
return compress_data
