SVD Image Compression
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About This MicroSim
This visualization demonstrates image compression using SVD by showing:
- Original image as a grayscale matrix
- Rank-k approximation using truncated SVD
- Error image (difference between original and compressed)
- Singular value spectrum showing which values are kept
Key Concepts
- Images can be represented as matrices (pixel values)
- SVD finds the "most important" directions in the image
- Keeping only top k singular values compresses the image
- Larger singular values capture more of the image structure
How to Use
- Select a pattern to generate different test images
- Adjust rank k using the slider to control compression
- Observe how image quality changes with k
- Watch the singular value spectrum to see truncation point
Statistics Explained
| Metric | Meaning |
|---|---|
| Compression | How many times smaller the storage |
| Error | Frobenius norm error as percentage |
| Variance | Percentage of total variance captured |
| Storage | Actual elements stored |
Learning Objectives
After using this MicroSim, students will be able to:
- Apply SVD for image compression
- Understand the quality-storage tradeoff
- Interpret singular value spectra
- Choose appropriate truncation level
References
- Chapter 7: Matrix Decompositions - Low-Rank Approximation
- Eckart-Young Theorem