Image Compression using Singular Value Decomposition (SVD)

This project demonstrates how Singular Value Decomposition (SVD) can be used to compress grayscale images by retaining only the most significant singular values. The technique is implemented in Python using NumPy and skimage.

Overview

• Load a high-resolution RGB image from the web
• Convert it to grayscale and resize to 256x256 for simplicity
• Apply SVD to decompose the image matrix
• Reconstruct compressed versions of the image using top k singular values
• Automatically find the optimal k based on:
  • Energy retention ≥ 95%
  • SSIM ≥ 0.90
• Visualize:
  • Original vs Compressed image
  • Singular values
  • Energy retention vs number of components k

Compression Metrics

• Energy Retention: Measures how much of the image’s information is preserved using the top k singular values.
• SSIM (Structural Similarity Index): Measures the perceptual similarity between the original and compressed image.

Optimal k Selection

The script automatically selects the smallest k that satisfies both:

• Energy retention ≥ 95%
• SSIM ≥ 0.90

This balances image quality and compression efficiency.

📷 Example Output

Original Image	Compressed Image
	Generated by script

Note: The actual image used is converted to grayscale and resized in the script.

Project Structure

IC_AdaptiveSVD.ipynb # Main script README.md # This file

Requirements

• numpy
• matplotlib
• scikit-image

Install with:

pip install numpy matplotlib scikit-image