SVD Image Compression (2D) — Singular Value Decomposition

Test image

Rank

Rank k 8

Show singular-value spectrum

Statistics

Rank used

Variance captured

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Compression ratio

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Reconstruction error

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SVD: any matrix A = UΣVᵀ. The rank-k reconstruction uses only the top k singular values: A_k = Σᵢ₌₁ᵏ σᵢ uᵢ vᵢᵀ. Compression ratio = k(m+n+1)/(mn). By the Eckart–Young theorem this is the mathematically optimal rank-k approximation in the Frobenius norm.

rank 8/32 · error — · ratio —