Transform-Based Image Processing

This project demonstrates image compression techniques using two fundamental transforms: the Discrete Wavelet Transform (DWT) and the Fast Fourier Transform (FFT). It provides Jupyter notebooks and sample assets to visualize, experiment with, and understand the effects of these transforms on image compression and reconstruction.

In this project, two sample images are used: sample1.jpg, which is a standard image to visualize the compression process, and sample2.jpg, which is a brain MRI image.

Sample 1	Sample 2

Features

• DWT Image Compression:
  • Visualizes DWT coefficients and their partitioning.
  • Demonstrates image compression by thresholding or partitioning DWT coefficients.
  • Shows the effect of coefficient manipulation on reconstructed images.
• FFT Image Compression:
  • Visualizes magnitude and phase of FFT.
  • Demonstrates compression by manipulating FFT magnitude.
  • Shows the effect of magnitude changes on image reconstruction.
• Sample Assets:
  • Includes example images and results for both DWT and FFT methods.

Directory Structure

assets/
  DWT/         # DWT sample images and results
  FFT/         # FFT sample images and results
FFT_magnitude.ipynb                # FFT magnitude analysis notebook
Sample1_DWT_Image_Compression.ipynb # DWT compression notebook (Sample 1)
Sample1_FFT_Image_Compression.ipynb # FFT compression notebook (Sample 1)
Sample2_DWT_Image_Compression.ipynb # DWT compression notebook (Sample 2)
Sample2_FFT_Image_Compression.ipynb # FFT compression notebook (Sample 2)
Transform-Based-Image-Processing (DWT and FFT Image Compression).pdf # Project report

Requirements

• Python 3.x
• numpy
• matplotlib
• imageio
• scikit-image (skimage)
• Jupyter Notebook

Install dependencies with:

pip install numpy matplotlib imageio scikit-image jupyter

Usage

1. Clone the repository and navigate to the project directory.
2. Launch Jupyter Notebook:

   jupyter notebook

3. Open and run the notebooks:
   • Sample1_DWT_Image_Compression.ipynb and Sample2_DWT_Image_Compression.ipynb for DWT-based compression.
   • Sample1_FFT_Image_Compression.ipynb, Sample2_FFT_Image_Compression.ipynb, and FFT_magnitude.ipynb for FFT-based compression and analysis.
4. Explore the assets/ directory for sample images and results.

Results

• DWT: See assets/DWT/ for original, coefficient, and compressed images.
• FFT: See assets/FFT/ for original, magnitude, and compressed images.

Sample2 FFT Compressed Images and Magnitude

Below is a table displaying the compressed images from Sample2_FFT_Image_Compression.ipynb and their corresponding FFT magnitude visualizations. Each compressed image is shown above its magnitude plot.

Compressed Image	Magnitude Plot

Sample1 DWT Compressed Images

Below is a table displaying the original, DWT coefficients, and compressed images from Sample1_DWT_Image_Compression.ipynb. All images are located in assets/DWT/.

Original Image	DWT Coefficients	Compressed Image

License

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