#!/usr/bin/env python3
"""
Provide structured illumination support.
Created on Sun Jan 9 17:39:02 2022
@author: Nicola VIGANÒ, Computational Imaging group, CWI, The Netherlands,
and ESRF - The European Synchrotron, Grenoble, France
"""
import copy as cp
from abc import ABC, abstractmethod
from collections.abc import Sequence
from typing import Union
import matplotlib.pyplot as plt
import numpy as np
import scipy.linalg as spalg
from numpy.typing import DTypeLike, NDArray
from tqdm.auto import tqdm
from . import operators, processing
NDArrayInt = NDArray[np.integer]
[docs]def reorder_masks(masks: NDArray, buckets: NDArray, shift: int) -> tuple[NDArray, NDArray]:
"""Reorder masks, with a simple rot-n algorithm.
Parameters
----------
masks : NDArray
The masks to re-order.
buckets : NDArray
The corresponding buckets.
shift : int
The length of the shift.
Returns
-------
Tuple[NDArray, NDArray]
The reordered masks and buckets.
"""
masks_shape = masks.shape
masks = masks.reshape([-1, *masks_shape[-2:]])
masks = np.roll(masks, -shift, axis=0)
buckets = np.roll(buckets, -shift)
return masks.reshape(masks_shape), buckets
[docs]def decompose_qr_masks(masks: NDArray, verbose: bool = False) -> tuple[NDArray, NDArray]:
"""Compute QR decomposition of the given masks.
Parameters
----------
masks : NDArray
The masks to decompose
verbose : bool, optional
Whether to emite verbose output, by default False
Returns
-------
Tuple[NDArray, NDArray]
The Q and R components.
"""
masks_shape = masks.shape
masks = masks.reshape([-1, np.prod(masks_shape[-2:])])
if verbose:
print("Computing QR decomposition")
Q, R = np.linalg.qr(masks.transpose())
Rt = R.transpose()
Qt = Q.transpose()
if verbose:
print("Computing inversion of R (fast, because triangular)")
R1t = np.linalg.inv(Rt)
return Qt.reshape(masks_shape), R1t
[docs]def estimate_resolution(masks: NDArray, verbose: bool = True, plot_result: bool = True) -> tuple[float, float]:
"""Estimate the mask collection resolution through auto-correlation.
Parameters
----------
masks : NDArray
The list of encoding masks
verbose : bool, optional
Whether to produce verbose output, by default True
plot_result : bool, optional
Whether to plot the results, by default True
Returns
-------
tuple[float, float]
The mean and minimum HWHM of the auto-correlation functions for all the masks.
"""
masks = masks.reshape([-1, *masks.shape[-2:]])
resolutions = np.zeros(len(masks))
for ind, mask in enumerate(tqdm(masks, desc="Computing auto-correlations", disable=not verbose)):
_, auto_corr = processing.misc.norm_cross_corr(mask, plot=False)
point = processing.misc.lines_intersection(auto_corr, 0.5, position="first")
resolutions[ind] = point[0] if point is not None else 0
res_mean = resolutions.mean()
res_min = resolutions.min()
if plot_result:
fig, axs = plt.subplots(1, 1, figsize=[9, 4])
axs.plot(resolutions, label="HWHM auto-correlation")
axs.hlines(res_mean, 0, len(resolutions), colors=["C1"], label=f"Mean ({res_mean:.3})")
axs.hlines(res_min, 0, len(resolutions), colors=["C2"], label=f"Min ({res_min:.3})")
axs.grid()
axs.legend()
fig.tight_layout()
plt.show(block=False)
return res_mean, res_min
[docs]class MaskCollection:
"""Define mask collection class."""
masks_enc: NDArray
masks_dec: NDArray
mask_dims: int
mask_support: NDArrayInt
mask_type: str
def __init__(
self,
masks_enc: NDArray,
masks_dec: Union[NDArray, None] = None,
mask_dims: int = 2,
mask_type: str = "measured",
mask_support: Union[None, Sequence[int], NDArrayInt] = None,
) -> None:
"""Initialize mask collection.
Parameters
----------
masks_enc : NDArray
The encoding masks.
masks_dec : NDArray | None, optional
The decoding masks. The default (None) will assume them identical to the encoding masks.
mask_dims : int, optional
The dimensions of a single mask. The feault is 2.
mask_type : str, optional
The type of masks. The default is "measured".
mask_support : Sequence[int] | NDArray[np.integer] | None, optional
The extent of the mask support in pixels. The default (None) will consider it equal to the FoV.
"""
self.mask_dims = mask_dims
# TODO: check sizes of masks
self.masks_enc = masks_enc
self.masks_dec = masks_dec if masks_dec is not None else masks_enc
# TODO: check the decoding masks are consistent with the encoding masks
self.mask_type = mask_type
# TODO: check support is honored
if mask_support is not None:
self.mask_support = np.array(mask_support, ndmin=1, dtype=int)
else:
self.mask_support = np.array(self.shape_FoV, ndmin=1, dtype=int)
@property
def shape_FoV(self) -> Sequence[int]:
"""Return the mask shape.
Returns
-------
Sequence[int]
The mask shape.
"""
return self.masks_enc.shape[-self.mask_dims :]
@property
def shape_shifts(self) -> Sequence[int]:
"""Compute the shape of the available shifts.
Returns
-------
Sequence[int]
The shape of the available shifts.
"""
return self.masks_enc.shape[: -self.mask_dims]
@property
def num_buckets(self) -> int:
"""Compute the total number of available buckets.
Returns
-------
int
The total number of buckets.
"""
return int(np.prod(self.shape_shifts))
[docs] def info(self) -> str:
"""
Return the mask info.
Returns
-------
str
Mask info string.
"""
return self.mask_type
[docs] def upper(self) -> str:
"""
Return the upper case name of the mask.
Returns
-------
str
Upper case string name of the mask.
"""
return self.mask_type.upper()
[docs] def lower(self) -> str:
"""
Return the lower case name of the mask.
Returns
-------
str
Lower case string name of the mask.
"""
return self.mask_type.lower()
[docs] def get_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Return the requested mask.
Parameters
----------
mask_inds_vu : Union[Sequence, NDArray]
The mask position.
mask_encoding : bool, optional
Whether it is an encoding or decoding mask, by default True
Returns
-------
NDArray
The requested mask.
"""
if mask_encoding is True:
mask = self.masks_enc
else:
mask = self.masks_dec
return mask[tuple(mask_inds_vu)]
[docs] def get_QR_decomposition(self, buckets: NDArray, shift: int = 0) -> tuple["MaskCollection", NDArray]:
"""Compute and return the QR decomposition of the masks.
Parameters
----------
buckets : NDArray
The buckets corresponding to the masks.
shift : int, optional
Index of the first mask, by default 0.
Returns
-------
Tuple[MaskCollection, NDArray]
The new mask collection and the matrix for modifying buckets accordingly.
Raises
------
ValueError
In case the masks have encoding-decoding form.
"""
if np.any(self.masks_dec != self.masks_enc):
raise ValueError("Cannot compute QR decomposition of masks that have encoding and decoding forms.")
new_masks = cp.deepcopy(self)
new_buckets = cp.deepcopy(buckets)
if shift != 0:
new_masks.masks_enc, new_buckets = reorder_masks(new_masks.masks_enc, new_buckets, shift=shift)
new_masks.masks_enc, R1t = decompose_qr_masks(new_masks.masks_enc)
new_masks.masks_dec = new_masks.masks_enc
new_buckets = R1t.dot(new_buckets)
return new_masks, new_buckets
[docs] def bin_masks(self, binning: float) -> "MaskCollection":
"""Bin the masks.
Parameters
----------
binning : float
The binning size.
Returns
-------
MaskCollection
A new collection of binned masks.
"""
new_masks = cp.deepcopy(self)
new_masks.masks_enc = processing.pre.bin_imgs(new_masks.masks_enc, binning=binning)
new_masks.masks_dec = processing.pre.bin_imgs(new_masks.masks_dec, binning=binning)
return new_masks
[docs] def inspect_masks(self, mask_inds_vu: Union[None, Sequence[int], NDArrayInt] = None):
"""Inspect the encoding and decoding masks at the requested shifts.
Parameters
----------
mask_inds_vu : Sequence[int] | NDArray[np.integer] | None, optional
The requested axes shifts. The default (None) is the first mask.
"""
if mask_inds_vu is None:
mask_inds_vu = [0] * len(self.shape_shifts)
mask_enc = self.get_mask(mask_inds_vu, mask_encoding=True)
mask_dec = self.get_mask(mask_inds_vu, mask_encoding=False)
f, axs = plt.subplots(1, 2)
f.suptitle("Base masks")
axs[0].imshow(mask_enc)
axs[0].set_title("Encoding")
axs[1].imshow(mask_dec)
axs[1].set_title("Decoding")
plt.show(block=False)
[docs]class MaskGenerator(ABC):
"""Define mask generation interface."""
shape_FoV: NDArrayInt
shape_mask: NDArrayInt
shape_shifts: NDArrayInt
transmittance: float
dtype: DTypeLike
_enc_dec_mismatch: bool
__mask_name__ = "generated"
def __init__(
self,
shape_FoV: Union[Sequence[int], NDArrayInt],
shape_mask: Union[Sequence[int], NDArrayInt],
shape_shifts: Union[Sequence[int], NDArrayInt],
transmittance: float = 1.0,
dtype: DTypeLike = np.float32,
) -> None:
"""Initialize mask collection.
Parameters
----------
shape_FoV : Sequence[int] | NDArray[np.integer]
The shape of the field-of-view.
shape_mask : Sequence[int] | NDArray[np.integer]
The shape of the masks.
shape_shifts : Sequence[int] | NDArray[np.integer]
The shape of the shifts to generate.
transmittance : float
The maximum transmittance of the structuring elements.
dtype : DTypeLike
The dtype of the created masks.
"""
self.shape_FoV = np.array(shape_FoV, dtype=int)
self.shape_mask = np.array(shape_mask, dtype=int)
self.shape_shifts = np.array(shape_shifts, dtype=int)
self.transmittance = transmittance
self.dtype = dtype
self._enc_dec_mismatch = False
[docs] def info(self) -> str:
"""
Return the mask info.
Returns
-------
str
Mask info string.
"""
return self.__mask_name__
def __repr__(self) -> str:
"""Produce the string representation of the object.
Returns
-------
str
The string representation.
"""
return self.__class__.__name__ + " {\n" + ",\n".join([f" {k} = {v}" for k, v in self.__dict__.items()]) + "\n}"
@property
def num_buckets(self) -> int:
"""Compute the number of buckets.
Returns
-------
int
The number of buckets.
"""
return int(np.prod(self.shape_shifts))
def _init_FoV_mm(self, FoV_size_mm: Union[float, Sequence[float], NDArray], req_res_mm: float) -> NDArrayInt:
self.FoV_size_mm = np.array(FoV_size_mm, ndmin=1)
num_points = np.ceil(self.FoV_size_mm / req_res_mm).astype(int)
self.feature_size_mm = self.FoV_size_mm / num_points
return num_points
[docs] def generate_collection(self, buckets_fraction: float = 1, shift_type: str = "sequential") -> MaskCollection:
"""Generate the mask collection.
Parameters
----------
buckets_fraction : float, optional
The fraction of buckets to generate, by default 1
shift_type : str, optional
The type of shift to implement, by default "sequential"
abs_fraction : float, optional
The attenuation fraction of the pixels
Returns
-------
MaskCollection
The generated mask collection.
Raises
------
ValueError
In case of wrong shift type.
"""
if shift_type.lower() == "random":
num_chosen_buckets = np.ceil(self.num_buckets * buckets_fraction).astype(int)
disp_v, disp_u = self.get_random_shifts(num_chosen_buckets)
elif shift_type.lower() == "interval":
interval = np.ceil(1 / buckets_fraction).astype(int)
disp_v, disp_u = self.get_interval_shifts(interval)
num_chosen_buckets = len(disp_v)
elif shift_type.lower() == "sequential":
num_chosen_buckets = np.ceil(self.num_buckets * buckets_fraction).astype(int)
disp_v, disp_u = self.get_sequential_shifts(num_chosen_buckets)
else:
raise ValueError('Wrong shift_type: "%s". Available options: {random} | interval | sequential.' % shift_type)
gen_masks_enc = self._generate_masks(disp_v, disp_u, mask_encoding=True)
gen_masks_dec = self._generate_masks(disp_v, disp_u, mask_encoding=False) if self._enc_dec_mismatch else None
print("Using %d masks over %d" % (num_chosen_buckets, self.num_buckets))
return MaskCollection(
gen_masks_enc,
gen_masks_dec,
mask_type=self.__mask_name__,
mask_support=self.shape_mask,
mask_dims=len(self.shape_FoV),
)
def _apply_transmission(self, masks: NDArray) -> NDArray:
return 1 - (1 - masks) * self.transmittance
[docs] @abstractmethod
def generate_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Produce the shifted masks.
Parameters
----------
mask_inds_vu : tuple | list | NDArray
The vertical and horizontal shifts.
mask_encoding : bool, optional
Is the mask encoding (False = decoding). The default is True.
Returns
-------
NDArray
The shifted mask.
"""
def _generate_masks(
self, shifts_v: Union[Sequence, NDArray], shifts_u: Union[Sequence, NDArray], mask_encoding: bool = True
) -> NDArray:
"""Produce all the masks.
Parameters
----------
shifts_v : tuple | list | NDArray
List of all the vertical shifts.
shifts_u : tuple | list | NDArray
List of all the horizontal shifts.
mask_encoding : bool, optional
Are the masks encoding (False = decoding). The default is True.
abs_fraction : float, optional
Absorption fraction of the mask elements. The default is 1.
Returns
-------
NDArray
The collection of all the shifted masks.
"""
masks = [self.generate_mask([v, u], mask_encoding) for v, u in zip(shifts_v, shifts_u)]
return np.stack(masks, axis=0) # .reshape([*self.shift_shape, *self.FoV_shape])
[docs] def get_interval_shifts(
self, interval: Union[int, Sequence[int], NDArray], axes_order: Sequence[int] = (-2, -1)
) -> Sequence[NDArray]:
"""Produce shifts for the "interval" shift type.
Parameters
----------
interval : int | tuple(int, int) | list(int, int)
The shift interval.
axes_order : int | tuple | list, optional
Order of the axes to shift. The default is (-2, -1).
Returns
-------
tuple
The collection of shifts.
"""
interval = np.array(interval, dtype=int)
if interval.size == 1:
interval = np.tile(interval, len(axes_order))
disps = [np.arange(0, self.shape_shifts[ax], interval[ii]) for ii, ax in enumerate(axes_order)]
disps = np.meshgrid(*disps, indexing="ij")
return [disp.flatten() for disp in disps]
[docs] def get_random_shifts(self, num_shifts: int, axes_order: Sequence[int] = (-2, -1)) -> Sequence[NDArray]:
"""Produce shifts for the "random" shift type.
Parameters
----------
num_shifts : int
Number of shifts.
Returns
-------
NDArray
The collection of shifts.
"""
max_disps = np.prod(self.shape_shifts)
if num_shifts > max_disps:
print("Warning, too many shifts. Truncating to: %d" % max_disps)
num_shifts = np.fmin(num_shifts, max_disps)
disps = self.get_interval_shifts(interval=1, axes_order=axes_order)
perms = np.random.permutation(np.prod(self.shape_shifts))[:num_shifts]
return [disp[perms] for disp in disps]
[docs] def get_sequential_shifts(
self, num_shifts: Union[int, None] = None, axes_order: Sequence[int] = (-2, -1)
) -> Sequence[NDArray]:
"""Produce shifts for the "sequential" shift type.
Parameters
----------
num_shifts : int, optional
Number of shifts. The default is None.
axes_order : tuple | list | NDArray, optional
Order of the axes to shift. The default is (-2, -1).
Returns
-------
NDArray
The collection of shifts.
"""
disps = self.get_interval_shifts(interval=1, axes_order=axes_order)
if num_shifts is not None:
disps = [disp[:num_shifts] for disp in disps]
return disps
[docs]class MaskGeneratorPoint(MaskGenerator):
"""Pencil beam masks generator class."""
__mask_name__ = "pencil"
def __init__(self, FoV_size_mm: Union[float, Sequence[float], NDArray], req_res_mm: float = 1.0):
"""Initialize the pencil beam mask collection.
Parameters
----------
FoV_size_mm : float
Size of the Field-of-View in millimiters.
req_res_mm : float
Requested resolution in millimiters.
"""
num_points = self._init_FoV_mm(FoV_size_mm, req_res_mm)
super().__init__(num_points, [1, 1], num_points)
[docs] def generate_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Produce the shifted masks.
Parameters
----------
mask_inds_vu : tuple | list | NDArray
The vertical and horizontal shifts.
mask_encoding : bool, optional
Is the mask encoding (False = decoding). The default is True.
Returns
-------
NDArray
The shifted mask.
"""
mask = np.zeros(self.shape_FoV, dtype=self.dtype)
mask[mask_inds_vu[0], mask_inds_vu[1]] = 1.0
return self._apply_transmission(mask)
[docs]class MaskGeneratorBernoulli(MaskGenerator):
"""Bernoulli mask generator class."""
__mask_name__ = "bernoulli"
def __init__(self, FoV_size_mm: Union[float, Sequence[float], NDArray], req_res_mm: float = 1.0):
"""
Bernulli masks collection class.
It computes and stores the original mask pattern for a given resolution and Field-ofView.
Parameters
----------
FoV_size_mm : float
DESCRIPTION.
req_res_mm : float
DESCRIPTION.
"""
num_points = self._init_FoV_mm(FoV_size_mm, req_res_mm)
super().__init__(num_points, num_points, num_points)
[docs] def generate_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Produce the shifted masks.
Parameters
----------
mask_inds_vu : tuple | list | NDArray
The vertical and horizontal shifts.
mask_encoding : bool, optional
Is the mask encoding (False = decoding). The default is True.
Returns
-------
NDArray
The shifted mask.
"""
mask = np.random.randint(0, 2, size=self.shape_FoV).astype(self.dtype)
return self._apply_transmission(mask)
[docs]class MaskGeneratorHalfGaussian(MaskGenerator):
"""Half-Gaussian mask generator class."""
__mask_name__ = "half-gaussian"
def __init__(self, FoV_size_mm: Union[float, Sequence[float], NDArray], req_res_mm: float = 1.0):
"""
Half Gaussian masks collection class.
It computes and stores the original mask pattern for a given resolution and Field-ofView.
Parameters
----------
FoV_size_mm : float
DESCRIPTION.
req_res_mm : float
DESCRIPTION.
"""
num_points = self._init_FoV_mm(FoV_size_mm, req_res_mm)
super().__init__(num_points, num_points, num_points)
[docs] def generate_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Produce the shifted masks.
Parameters
----------
mask_inds_vu : tuple | list | NDArray
The vertical and horizontal shifts.
mask_encoding : bool, optional
Is the mask encoding (False = decoding). The default is True.
Returns
-------
NDArray
The shifted mask.
"""
mask = np.abs(np.random.randn(*self.shape_FoV)).astype(self.dtype)
return self._apply_transmission(mask)
[docs]class MaskGeneratorMURA(MaskGenerator):
"""MURA mask generator class."""
__mask_name__ = "mura"
def __init__(self, FoV_size_mm: float, req_res_mm: float = 1.0):
"""
MURA masks collection class.
Parameters
----------
FoV_size_mm : float
DESCRIPTION.
req_res_mm : float
DESCRIPTION.
"""
self.FoV_size_mm = np.array([FoV_size_mm, FoV_size_mm])
base_points = int(np.ceil((FoV_size_mm / req_res_mm - 1) / 4))
num_points = 4 * base_points + 1
self.feature_size_mm = self.FoV_size_mm / num_points
sq = np.mod(np.arange(num_points) ** 2, num_points)
mask_1d = np.zeros(num_points)
mask_1d[sq[1:]] = 1
self.masks_enc = mask_1d[:, None] * mask_1d[None, :] + ((1 - mask_1d[:, None]) * (1 - mask_1d[None, :]))
self.masks_enc[0, :] = 0
self.masks_enc[1:, 0] = 1
self.masks_dec = self.masks_enc.copy()
self.masks_dec[0, 0] = 1
super().__init__([num_points, num_points], [num_points, num_points], [num_points, num_points])
self._enc_dec_mismatch = True
[docs] def generate_mask(self, mask_inds_vu: Union[Sequence, NDArray], mask_encoding: bool = True) -> NDArray:
"""Produce the shifted masks.
Parameters
----------
mask_inds_vu : tuple | list | NDArray
The vertical and horizontal shifts.
mask_encoding : bool, optional
Is the mask encoding (False = decoding). The default is True.
Returns
-------
NDArray
The shifted mask.
"""
if mask_encoding:
mask = self.masks_enc
else:
mask = self.masks_dec
for ii, ind in enumerate(mask_inds_vu):
mask = np.roll(mask, ind, axis=ii)
return self._apply_transmission(mask)
[docs] @staticmethod
def compute_possible_mask_sizes(FoV_size: int) -> NDArray:
"""Compute MURA masks sizes.
MURA masks require specific edge sizes: prime numbers _x_ that also
satisfy the rule: _x_ = 4 * _l_ + 1, where _l_ is integer.
Parameters
----------
FoV_size : int
Edge size of the FoV in pixels.
Returns
-------
NDArray
Array of all possible MURA mask sizes in that range.
"""
def test_prime(x):
div_val = x % np.arange(2, x // 2)
return not np.any(div_val == 0)
max_possible_val = (FoV_size - 1) // 4
test_values = np.arange(1, max_possible_val) * 4 + 1
primes = np.array([test_prime(x) for x in test_values])
return test_values[primes]
[docs]class ProjectorGhostImaging(operators.ProjectorOperator):
"""Projector class for the ghost imaging reconstructions."""
mc: MaskCollection
def __init__(self, mask_collection: MaskCollection):
"""
Initialize the Ghost Imaging projector class.
Parameters
----------
mask_collection : MaskCollection
Container of the masks.
"""
self.mc = mask_collection
self._axes_shifts = np.arange(len(self.mc.shape_shifts))
self.col_sum = np.abs(self.mc.masks_dec).sum(axis=tuple(self._axes_shifts))
self._axes_fov = np.arange(-len(self.mc.shape_FoV), 0)
self.row_sum = np.sqrt(np.abs(self.mc.masks_enc * self.mc.masks_dec)).sum(axis=tuple(self._axes_fov))
self.vol_shape = self.mc.masks_enc.shape[-2:]
self.prj_shape = np.array(self.mc.num_buckets, ndmin=1)
super().__init__()
[docs] def fp(self, image: NDArray) -> NDArray:
"""Compute forward-projection (prediction) of the bucket values.
Parameters
----------
image : NDArray
The image for which we want to predict the bucket values.
Returns
-------
NDArray
The predicted bucket values.
"""
masks_shape = [np.prod(self.mc.shape_shifts), np.prod(self.mc.shape_FoV)]
image_shape = [*image.shape[: -self.mc.mask_dims], np.prod(image.shape[-self.mc.mask_dims :])]
return np.squeeze(image.reshape(image_shape).dot(self.mc.masks_enc.reshape(masks_shape).T))
# return np.sum(self.masks_enc * image, axis=(-2, -1))
[docs] def bp(self, bucket_vals: NDArray) -> NDArray:
"""Compute back-projection of the bucket values.
Parameters
----------
bucket_vals : NDArray
The list of bucket values.
subtract_mean : bool, optional
Whether to subtract the mean of the values. The default is False.
Returns
-------
NDArray
Back-projected image.
"""
masks_shape = [np.prod(self.mc.shape_shifts), np.prod(self.mc.shape_FoV)]
out_shape = [*bucket_vals.shape[:-1], *self.mc.shape_FoV]
masks_in = self.mc.masks_dec.reshape(masks_shape)
img_out: NDArray = bucket_vals.dot(masks_in)
return img_out.reshape(out_shape)
# return np.sum(bucket_vals[..., None, None] * self.masks_dec, axis=-3, keepdims=True)
[docs] def adjust_sampling_scaling(self, image: NDArray) -> NDArray:
"""Adjust reconstruction scaling and bias, due to the undersampling.
Parameters
----------
image : NDArray
Unscaled image.
Returns
-------
NDArray
Scaled image.
"""
sampling_ratio = self.mc.num_buckets / np.prod(self.mc.shape_FoV)
image_f: NDArray = np.fft.rfftn(image, axes=tuple(self._axes_fov), norm="ortho")
rec_f_shape = np.array(image_f.shape)[list(self._axes_fov)]
sampling_filter = np.ones(rec_f_shape, dtype=image.dtype) / sampling_ratio
sampling_filter[0, 0] = 1
image_f *= sampling_filter
return np.fft.irfftn(image_f, s=self.mc.shape_FoV, axes=tuple(self._axes_fov), norm="ortho")
[docs] def fbp(self, bucket_vals: NDArray, use_lstsq: bool = True, adjust_scaling: bool = True) -> NDArray:
"""Compute cross-correlation reconstruction of the bucket values.
Parameters
----------
bucket_vals : NDArray
The bucket vales to reconstruct.
Returns
-------
NDArray
The reconstructed image.
"""
# return self.bp(bucket_vals - np.mean(bucket_vals)) + np.mean(bucket_vals) * np.mean(self.col_sum)
if np.any(self.mc.masks_enc != self.mc.masks_dec) and not use_lstsq:
img = self.bp(bucket_vals)
else:
masks = self.mc.masks_enc.reshape([-1, np.prod(self.mc.shape_FoV)])
result = spalg.lstsq(masks, bucket_vals)
img: NDArray = result[0]
img = img.reshape(self.mc.shape_FoV)
if adjust_scaling:
img = self.adjust_sampling_scaling(img)
return img
[docs] def absolute(self):
"""Compute the absolute value of the projection operator coefficients.
Returns
-------
Op_a : ProjectorGhostImaging
The absolute value of the projector.
"""
Op_a = cp.deepcopy(self)
Op_a.mc.masks_enc = np.abs(Op_a.mc.masks_enc)
Op_a.mc.masks_dec = np.abs(Op_a.mc.masks_dec)
return Op_a