Image SVD Low-Rank Approximation

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Normalized Singular Value Decay

The vertical axis is σ / σ₁; faster decay indicates stronger low-rank structure.

R G B

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Input Image Matrix -
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Rank-Truncated Approximation r = -
Waiting for SVD
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\(E_r=\dfrac{\sum_c\sum_{i=1}^{r}\sigma_{c,i}^{2}}{\sum_c\sum_i\sigma_{c,i}^{2}}\)
Retained Energy
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\(\rho_r=\dfrac{r(h+w+1)}{hw}\)
Low-Rank Storage Ratio
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\(\varepsilon_r=\dfrac{\lVert A-A_r\rVert_F}{\lVert A\rVert_F}=\sqrt{1-E_r}\)
Relative Frobenius Error