Image Fusion and Denoising using Haar Wavelet Transform

This project demonstrates image fusion and denoising techniques using the Haar wavelet transform and Non-Local Means denoising method. The goal is to merge two images and reduce noise while preserving important features.

Prerequisites

Before running the code, make sure you have the following Python packages installed:

• opencv-python - for image processing
• scikit-image - for image enhancement and restoration
• PyWavelets - for wavelet decomposition and reconstruction
• matplotlib - for visualizing images

You can install these dependencies by running:

pip install opencv-python scikit-image PyWavelets matplotlib

Steps Involved

1. Image Upload and Preprocessing:

   • Two grayscale images are uploaded and preprocessed using histogram equalization to enhance their contrast.

2. Wavelet Decomposition:

   • Both images are decomposed into wavelet coefficients (LL, LH, HL, HH) using the 2D Haar wavelet transform.

3. Image Fusion:

   • The approximation coefficients (LL) are fused by averaging both images.
   • The detail coefficients (LH, HL, HH) are fused by taking the maximum value at each corresponding position.

4. Reconstruction:

   • The fused image is reconstructed by applying the inverse Haar wavelet transform to the fused coefficients.

5. Denoising:

   • The fused image is denoised using the Non-Local Means denoising method to reduce noise while preserving important image details.

6. Visualization:

   • The original images, enhanced images, fused image, and denoised image are displayed using matplotlib.

Running the Code

1. Upload the two image files (c08_1.tif and c08_2.tif) to the environment.
2. Run the code in a Python environment like Google Colab or Jupyter Notebook.
3. View the results in the output, which includes:
   • Original Images
   • Enhanced Images
   • Fused Image
   • Denoised Image

Example Code

import cv2
import numpy as np
import pywt
import matplotlib.pyplot as plt
from skimage import exposure, restoration

# Load images
img1 = cv2.imread('c08_1.tif', cv2.IMREAD_GRAYSCALE)
img2 = cv2.imread('c08_2.tif', cv2.IMREAD_GRAYSCALE)

# Enhance images
img1_enhanced = exposure.equalize_hist(img1.astype(np.float32) / 255.0)
img2_enhanced = exposure.equalize_hist(img2.astype(np.float32) / 255.0)

# Perform Haar wavelet transform
coeffs1 = pywt.dwt2(img1_enhanced, 'haar')
coeffs2 = pywt.dwt2(img2_enhanced, 'haar')

# Extract coefficients
LL1, (LH1, HL1, HH1) = coeffs1
LL2, (LH2, HL2, HH2) = coeffs2

# Fusion of coefficients
LL_fused = (LL1 + LL2) / 2
LH_fused = np.maximum(LH1, LH2)
HL_fused = np.maximum(HL1, HL2)
HH_fused = np.maximum(HH1, HH2)

# Reconstruct fused image
fused_img = pywt.idwt2((LL_fused, (LH_fused, HL_fused, HH_fused)), 'haar')

# Denoise the fused image
denoised_img = restoration.denoise_nl_means(fused_img, h=0.1, fast_mode=True)

# Display images
fig, axs = plt.subplots(2, 3, figsize=(15, 10))
axs[0, 0].imshow(img1, cmap='gray')
axs[0, 0].set_title('Original Image 1')
axs[0, 1].imshow(img2, cmap='gray')
axs[0, 1].set_title('Original Image 2')
axs[0, 2].imshow(fused_img, cmap='gray')
axs[0, 2].set_title('Fused Image')
axs[1, 0].imshow(img1_enhanced, cmap='gray')
axs[1, 0].set_title('Enhanced Image 1')
axs[1, 1].imshow(img2_enhanced, cmap='gray')
axs[1, 1].set_title('Enhanced Image 2')
axs[1, 2].imshow(denoised_img, cmap='gray')
axs[1, 2].set_title('Denoised Image')

for ax in axs.ravel():
    ax.axis('off')
plt.tight_layout()
plt.show()

Results

• Enhanced Images: The images after histogram equalization, providing better contrast.
• Fused Image: The combined image that merges features from both images using wavelet fusion.
• Denoised Image: The image after noise reduction, making it clearer and more detailed.

License

This project is licensed under the MIT License - see the LICENSE file for details.