SVD Image Surgeon

Decompose any image rank by rank. Drag the slider to watch it reconstruct in real time.

A = UΞ£Vα΅€
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Click to upload or drag & drop an image onto this box

Large images are auto-resized for speed  Β·  JPG Β· PNG Β· WebP

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Rank k
β€”
Energy captured
β€”
Compression ratio
β€”
Max rank
β€”
Originalβ€”
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Upload to begin

Rank-k Reconstructionk = β€”
🧬

Will appear here

Rank k β€”
Energy captured by rank-k approximationβ€”
Singular Value Spectrum  Οƒβ‚ β‰₯ Οƒβ‚‚ β‰₯ … β‰₯ Οƒβ‚™

The math behind the magic

A = UΞ£Vα΅€  β‰ˆ  Ξ£i=1k Οƒα΅’Β·uα΅’vα΅’α΅€
Storage: full = mΓ—n  |  rank-k = k(m+n+1) per channel

Each color channel (R, G, B) is a matrix. SVD splits it into ranked patterns ordered by energy. Natural images are low-rank by nature β€” smooth regions and spatial correlations mean singular values drop rapidly. Try the checkerboard: its spectrum is flat (high rank, incompressible) β€” the perfect contrast to prove you understand the theory!