Dynamic Image Compression

You can see the Notebook here

The notebook demonstrates an image compression technique using Singular Value Decomposition (SVD). The core idea is to decompose an image into its constituent singular values and then reconstruct a compressed version using only the most significant singular values.

Benefits:

• Dynamic Compression: The algorithm dynamically determines the optimal number of singular values (k) required to achieve a desired image quality (in this case, a PSNR greater than 30 dB).
• Reduced Storage: By using a smaller number of singular values, the compressed image requires significantly less storage space compared to the original.
• Quantifiable Quality: The use of PSNR provides a objective metric to evaluate the quality of the compressed image.

Algorithm:

1. Load and Convert Image: The notebook loads an image and converts it to grayscale.
2. Perform SVD: Singular Value Decomposition is applied to the grayscale image matrix, resulting in three matrices: U, S (singular values), and Vt.
3. Determine Optimal k: The notebook iterates through different values of k (number of singular values) and calculates the PSNR for each reconstructed image. The minimum k that achieves a PSNR greater than the specified threshold (30 dB) is selected.
4. Reconstruct Image: The compressed image is reconstructed using the truncated U, S, and Vt matrices based on the optimal k.
5. Evaluate Compression: The compression ratio, final PSNR, and RMSE are calculated to assess the effectiveness of the compression.
6. Display Images: The original and compressed images are displayed for visual comparison.