Add wavelet-based image denoising example

DIRECTORY.md

@@ -336,6 +336,7 @@
     * [Rotation](digital_image_processing/rotation/rotation.py)
   * [Sepia](digital_image_processing/sepia.py)
   * [Test Digital Image Processing](digital_image_processing/test_digital_image_processing.py)
+  * [Wavelet Denoising](digital_image_processing/wavelet_denoising.py)
 
 ## Divide And Conquer
   * [Closest Pair Of Points](divide_and_conquer/closest_pair_of_points.py)

digital_image_processing/wavelet_denoising.py

@@ -0,0 +1,128 @@
+"""Wavelet-based image denoising example."""
+
+from __future__ import annotations
+
+import math
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pywt
+from skimage import data
+from skimage.metrics import peak_signal_noise_ratio
+
+
+def im2double(image: np.ndarray) -> np.ndarray:
+    """Return the image converted to ``float64`` precision.
+
+    If the input image already contains floating point values the image is
+    returned cast to ``float64`` without further scaling.  Integer images are
+    scaled to the ``[0, 1]`` range, matching MATLAB's :func:`im2double`
+    behaviour.
+    """
+
+    if np.issubdtype(image.dtype, np.floating):
+        return image.astype(np.float64)
+
+    info = np.iinfo(image.dtype)
+    return image.astype(np.float64) / info.max
+
+
+def normalize_img(image: np.ndarray) -> np.ndarray:
+    """Clip image data to the ``[0, 1]`` range."""
+
+    return np.clip(image, 0.0, 1.0)
+
+
+def denoise_image_wavelet(
+    original_img: np.ndarray,
+    noise_level: float = 0.1,
+    wavelet_name: str = "db4",
+    decomposition_level: int = 3,
+    rng: np.random.Generator | None = None,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Denoise an image using wavelet thresholding.
+
+    The function adds synthetic Gaussian noise to ``original_img`` and then
+    performs wavelet thresholding to suppress the noise.
+
+    Args:
+        original_img: Clean input image in the ``[0, 1]`` range.
+        noise_level: Standard deviation of the synthetic Gaussian noise.
+        wavelet_name: Name of the wavelet family to use.
+        decomposition_level: Number of wavelet decomposition levels.
+        rng: Optional ``numpy`` random number generator for reproducibility.
+
+    Returns:
+        A tuple ``(noisy_img, denoised_img)`` containing the noisy and
+        denoised images respectively.
+    """
+
+    if rng is None:
+        rng = np.random.default_rng()
+
+    original_img = im2double(original_img)
+
+    noisy_img = original_img + noise_level * rng.standard_normal(original_img.shape)
+    noisy_img = normalize_img(noisy_img)
+
+    coeffs = pywt.wavedec2(noisy_img, wavelet_name, level=decomposition_level)
+    coeffs_approx = coeffs[0]
+    coeffs_details = coeffs[1:]
+
+    detail_coeffs = [
+        detail_array.ravel()
+        for level_details in coeffs_details
+        for detail_array in level_details
+    ]
+    if not detail_coeffs:
+        msg = "Wavelet decomposition did not produce detail coefficients."
+        raise ValueError(msg)
+    all_detail_coeffs = np.concatenate(detail_coeffs)
+
+    sigma = np.median(np.abs(all_detail_coeffs)) / 0.6745
+    threshold = sigma * math.sqrt(2.0 * math.log(original_img.size))
+
+    denoised_details = [
+        tuple(pywt.threshold(detail_array, threshold, mode="soft") for detail_array in level_details)
+        for level_details in coeffs_details
+    ]
+    coeffs_denoised = [coeffs_approx, *denoised_details]
+
+    denoised_img = pywt.waverec2(coeffs_denoised, wavelet_name)
+    denoised_img = denoised_img[: original_img.shape[0], : original_img.shape[1]]
+    denoised_img = normalize_img(denoised_img)
+
+    return noisy_img, denoised_img
+
+
+def main() -> None:
+    """Run the wavelet denoising example and display the results."""
+
+    original_img = im2double(data.camera())
+    noisy_img, denoised_img = denoise_image_wavelet(original_img)
+
+    psnr_noisy = peak_signal_noise_ratio(original_img, noisy_img)
+    psnr_denoised = peak_signal_noise_ratio(original_img, denoised_img)
+
+    fig, axes = plt.subplots(1, 3, figsize=(18, 6))
+    ax = axes[0]
+    ax.imshow(original_img, cmap="gray")
+    ax.set_title("Original Image")
+    ax.axis("off")
+
+    ax = axes[1]
+    ax.imshow(noisy_img, cmap="gray")
+    ax.set_title(f"Noisy Image (PSNR: {psnr_noisy:.2f} dB)")
+    ax.axis("off")
+
+    ax = axes[2]
+    ax.imshow(denoised_img, cmap="gray")
+    ax.set_title(f"Denoised Image (PSNR: {psnr_denoised:.2f} dB)")
+    ax.axis("off")
+
+    plt.tight_layout()
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

pyproject.toml

@@ -16,11 +16,13 @@ dependencies = [
   "lxml>=5.3",
   "matplotlib>=3.9.3",
   "numpy>=2.1.3",
+  "PyWavelets>=1.6.0",
   "opencv-python>=4.10.0.84",
   "pandas>=2.2.3",
   "pillow>=11",
   "requests>=2.32.3",
   "rich>=13.9.4",
+  "scikit-image>=0.24.0",
   "scikit-learn>=1.5.2",
   "sphinx-pyproject>=0.3",
   "statsmodels>=0.14.4",

requirements.txt

@@ -6,12 +6,14 @@ keras
 lxml
 matplotlib
 numpy
+PyWavelets
 opencv-python
 pandas
 pdfkit
 pillow
 requests
 rich
+scikit-image
 scikit-learn
 sphinx_pyproject
 statsmodels