01.a. Acquisition operators (basic)

This tutorial shows how to simulate measurements using the spyrit.core.meas submodule.

All simulations are based on spyrit.core.meas.Linear base class that simulates linear measurements

\[m = Hx,\]

where \(H\in\mathbb{R}^{M\times N}\) is the acquisition matrix, \(x \in \mathbb{R}^N\) is the signal of interest, \(M\) is the number of measurements, and \(N\) is the dimension of the signal.

Important

The vector \(x \in \mathbb{R}^N\) represents a multi-dimensional array (e.g, an image \(X \in \mathbb{R}^{N_1 \times N_2}\) with \(N = N_1 \times N_2\)). Both variables are related through vectorization , i.e., \(x = \texttt{vec}(X)\).

1D Measurements

We instantiate a measurement operator from a matrix of shape (10, 15).

import torch
from spyrit.core.meas import Linear

H = torch.randn(10, 15)
meas_op = Linear(H)

We consider 3 signals of length 15

x = torch.randn(3, 15)

We apply the operator to the batch of images, which produces 3 measurements of length 10

m = meas_op(x)
print(m.shape)

torch.Size([3, 10])

We now plot the matrix-vector products

from spyrit.misc.disp import add_colorbar, noaxis
import matplotlib.pyplot as plt

f, axs = plt.subplots(1, 3, figsize=(10, 5))
axs[0].set_title("Forward matrix H")
im = axs[0].imshow(H, cmap="gray")
add_colorbar(im, "bottom")

axs[1].set_title("Signals x")
im = axs[1].imshow(x.T, cmap="gray")
add_colorbar(im, "bottom")

axs[2].set_title("Measurements m")
im = axs[2].imshow(m.T, cmap="gray")
add_colorbar(im, "bottom")

noaxis(axs)
# sphinx_gallery_thumbnail_number = 1

/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)
/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)
/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)

2D Measurements

We load a batch of images from the /images/ folder. Using the transform_gray_norm() function with the normalize=False argument returns images with values in (0,1).

import os
import torchvision
from spyrit.misc.statistics import transform_gray_norm

spyritPath = os.getcwd()
imgs_path = os.path.join(spyritPath, "images/")

# Grayscale images of size (32, 32), no normalization to keep values in (0,1)
transform = transform_gray_norm(img_size=32, normalize=False)

# Create dataset and loader (expects class folder :attr:'images/test/')
dataset = torchvision.datasets.ImageFolder(root=imgs_path, transform=transform)
dataloader = torch.utils.data.DataLoader(dataset, batch_size=7)

x, _ = next(iter(dataloader))

We crop the batch to get image of shape (9, 25).

x = x[:, :, :9, :25]
print(f"Shape of input images: {x.shape}")

Shape of input images: torch.Size([7, 1, 9, 25])

We plot the second image.

from spyrit.misc.disp import imagesc

imagesc(x[1, 0, :, :], "Image X")

/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)

We instantiate a measurement operator from a random matrix with shape (10, 9*25). To indicate that the operator works in 2D, we use the meas_shape argument.

H = torch.randn(10, 9 * 25)
meas_op = Linear(H, meas_shape=(9, 25))

We apply the operator to the batch of images, which produces a batch of measurement vectors of length 10.

m = meas_op(x)
print(m.shape)

torch.Size([7, 1, 10])

We now plot the matrix-vector products corresponding to the second image in the batch.

We first select the second image and the second measurement vector in the batch.

x_plot = x[1, 0, :, :]
m_plot = m[1]

Then we vectorize the image to get a 1D array of length 9*25.

x_plot = x_plot.reshape(1, -1)

print(f"Vectorised image with shape: {x_plot.shape}")

Vectorised image with shape: torch.Size([1, 225])

We finally plot the matrix-vector products \(m = H x = H \texttt{vec}(X)\).

from spyrit.misc.disp import add_colorbar, noaxis
import matplotlib.pyplot as plt

f, axs = plt.subplots(1, 3)
axs[0].set_title("Forward matrix H")
im = axs[0].imshow(H, cmap="gray")
# add_colorbar(im, "bottom")

axs[1].set_title("x = vec(X)")
im = axs[1].imshow(x_plot.mT, cmap="gray")
# add_colorbar(im, "bottom")

axs[2].set_title("Measurements m")
im = axs[2].imshow(m_plot.mT, cmap="gray")
# add_colorbar(im, "bottom")

noaxis(axs)

/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)
/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)
/home/docs/checkouts/readthedocs.org/user_builds/spyrit/envs/3.0.1/lib/python3.11/site-packages/matplotlib/cbook.py:684: DeprecationWarning: __array__ implementation doesn't accept a copy keyword, so passing copy=False failed. __array__ must implement 'dtype' and 'copy' keyword arguments. To learn more, see the migration guide https://numpy.org/devdocs/numpy_2_0_migration_guide.html#adapting-to-changes-in-the-copy-keyword
  x = np.array(x, subok=True, copy=copy)