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")

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")