Blind source separation (BSS) on blended photographs¶

We blend 5 grayscale photographs using a random mixing matrix and attempt to recover them using AMICA and FastICA.

from pathlib import Path
import numpy as np
import matplotlib.pyplot as plt
from PIL import Image
from sklearn.decomposition import FastICA

from amica import AMICA, datasets

Utilities¶

def load_grayscale_image(path: Path, size: tuple[int, int] | None = None) -> np.ndarray:
    img = Image.open(path).convert("L")
    if size:
        img = img.resize(size)
    return np.asarray(img, dtype=float) / 255.0


def plot_images(images: list[np.ndarray], title: str | None = None) -> None:
    n = len(images)
    fig, axes = plt.subplots(1, n, figsize=(3 * n, 3))

    if title:
        fig.suptitle(title, fontsize=14)

    for ax, img in zip(axes, images):
        ax.imshow(img, cmap="gray", interpolation="nearest")
        ax.set_xticks([])
        ax.set_yticks([])

    plt.tight_layout()
    plt.show()

Load source images¶

photos_dir = datasets.data_path() / "photos"
filenames = [
    "example2_baboon",
    "example2_cameraman",
    "example2_lena",
    "example2_mona",
    "example2_texture",
]

sources = [load_grayscale_image(photos_dir / fn) for fn in filenames]

# Common shape (ensure consistent size)
height, width = sources[0].shape

# Stack flattened as rows -> shape (n_sources, n_pixels)
S = np.vstack([src.ravel() for src in sources])
plot_images(sources, title="Source Images")

Mix sources with random mixing matrix¶

seed = 42
rng = np.random.default_rng(seed)
A = rng.random((5, 5))
X = A @ S  # shape (5, pixels)

mixed_images = [row.reshape(height, width) for row in X]
plot_images(mixed_images, title="Mixed Observations")

Recover with AMICA¶

amica = AMICA(random_state=seed, tol=.0001) # increase tol to match FastICA tolerance
S_amica = amica.fit_transform(X.T).T
recovered_amica = [row.reshape(height, width) for row in S_amica]

plot_images(recovered_amica, title="Recovered with AMICA")

INFO     | getting the mean ... - amica.linalg:pre_whiten
INFO     |  Getting the covariance matrix ... - amica.linalg:pre_whiten
INFO     | doing eigenvalue decomposition for 5 features ... - amica.linalg:pre_whiten
INFO     | minimum eigenvalues: [0.00243759 0.01114913] - amica.linalg:pre_whiten
INFO     | maximum eigenvalues: [0.47286901 0.03820661 0.0165536 ] - amica.linalg:pre_whiten
INFO     | num eigvals kept: 5 - amica.linalg:pre_whiten
INFO     | Sphering the data... - amica.linalg:pre_whiten
INFO     | numeigs = 5, nw = 5 - amica.linalg:pre_whiten
INFO     | 1: block size = 65536 - amica.core:solve
INFO     | Solving. (please be patient, this may take a while)... - amica.core:solve
INFO     | Iteration 1, lrate = 0.05000, LL = 0.4165154, nd = 0.1385838, D = 0.00007 0.00007 took 0.33 seconds - amica.core:optimize
INFO     | Iteration 2, lrate = 0.05000, LL = 0.4516854, nd = 0.0514464, D = 0.00006 0.00006 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 3, lrate = 0.05000, LL = 0.4582944, nd = 0.0353539, D = 0.00002 0.00002 took 0.30 seconds - amica.core:optimize
INFO     | Iteration 4, lrate = 0.05000, LL = 0.4601825, nd = 0.0402730, D = 0.00003 0.00003 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 5, lrate = 0.05000, LL = 0.4612398, nd = 0.0430717, D = 0.00014 0.00014 took 0.30 seconds - amica.core:optimize
INFO     | Iteration 6, lrate = 0.05000, LL = 0.4621110, nd = 0.0442121, D = 0.00035 0.00035 took 0.30 seconds - amica.core:optimize
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INFO     | Iteration 45, lrate = 0.05000, LL = 0.5397328, nd = 1.5716119, D = 0.04358 0.04358 took 0.20 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 46, lrate = 0.05000, LL = 0.2808522, nd = 0.7223066, D = 0.08576 0.08576 took 0.19 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 47, lrate = 0.05000, LL = 0.4731858, nd = 0.0845343, D = 0.06649 0.06649 took 0.21 seconds - amica.core:optimize
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INFO     | Starting Newton ... setting numdecs to 0 - amica.core:optimize
INFO     | Iteration 51, lrate = 0.10000, LL = 0.5328967, nd = 0.0346232, D = 0.04115 0.04115 took 0.20 seconds - amica.core:optimize
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INFO     | Iteration 125, lrate = 1.00000, LL = 0.6937141, nd = 0.0003389, D = 0.03192 0.03192 took 0.32 seconds - amica.core:optimize
INFO     | Iteration 126, lrate = 1.00000, LL = 0.6938046, nd = 0.0003545, D = 0.03194 0.03194 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 127, lrate = 1.00000, LL = 0.6938962, nd = 0.0003509, D = 0.03196 0.03196 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 128, lrate = 1.00000, LL = 0.6939892, nd = 0.0003642, D = 0.03198 0.03198 took 0.39 seconds - amica.core:optimize
INFO     | Exiting because likelihood increasing by less than 0.0001 for more than 5 iterations ... - amica.core:optimize
INFO     | Finished in 37.82 seconds - amica.core:optimize

Recover with FastICA¶

fastica = FastICA(n_components=5, random_state=seed)
S_fast = fastica.fit_transform(X.T).T
recovered_fastica = [row.reshape(height, width) for row in S_fast]

plot_images(recovered_fastica, title="Recovered with FastICA")

Total running time of the script: (0 minutes 39.832 seconds)

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