📦 SVD-Based Image Compression

A Python project that performs image compression using Singular Value Decomposition (SVD) on the RGB channels of a color image.

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📌 Features

• Reads and displays any color image
• Splits image into Red, Green, and Blue channels
• Applies SVD on each channel
• Reconstructs the image using the top k singular values
• Displays and saves the compressed image

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🖼️ Sample Output

• Original and compressed image comparison (shown via OpenCV GUI)
• Matrix shape and values printed for debugging and learning purposes

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🧠 How It Works

1. Image is split into RGB channels.
2. SVD is performed on each channel.
3. Each channel is reconstructed using only the top k singular values.
4. The channels are merged to create the compressed image.

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📁 Project Structure

svd_image_compression/
├── image_compression.py   # Main Python script
├── example.jpg            # (Optional) Sample input image
└── README.md              # This file

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🛠 Requirements

Install required packages using:

pip install numpy opencv-python

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🚀 How to Run

python image_compression.py

Then follow the prompts:

• Enter the path to your input image
• Enter the value of k (number of singular values to retain)
• Provide a save path for the compressed output

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✍️ Example Usage

Enter the image path: example.jpg
Enter the value of k: 50
Enter Output Path: ./output/

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📊 What is SVD Compression?

SVD helps reduce image size while retaining important features:

• Lower k means more compression (less detail).
• Higher k retains more image quality.

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📷 Sample Compression (k = 50 vs. k = 200)

k Value	File Size	Quality
50	Smaller	Blurry
200	Larger	Clear

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