Algorithm 1. Proposed muli-frame vignetting correction method

Input: Vignetted images $X={\left\{I_k\right\}}_{k=1}^N$, polynomial order $P$, and numerical constant $ϵ$.

Output: Estimated vignette field $\widehat{V}$ and corrected images ${\left\{I_{corr,k}\right\}}_{k=1}^N$.

1: Transform each image into the logarithmic domain: $D_k=\mathrm{l}\mathrm{o}\mathrm{g}\left(I_k+ϵ\right)$.

2: Vectorize $D_k$ and construct $D=\left[d_1,\dots ,d_N\right]$.

3: Estimate the shared low-rank component by solving $D=L+S$, where $L=v{\mathbf{1}}^T$.

4: Reshape $v$ to obtain the initial vignette field $B_0\left(x,y\right)$.

5: Smooth $B_0$ and fit a polynomial of order $P$ to obtain $\widehat{B}\left(x,y\right)$.

6: Recover the multiplicative vignette field: $\widehat{V}\left(x,y\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left(\widehat{B}\left(x,y\right)\right)$.

7: Calculate the correction gain $G\left(x,y\right)=1/\left(\widehat{V}\left(x,y\right)+ϵ\right)$.

8: Correct each frame: $I_{corr,k}=\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{p}\left(I_{k}G,0,L_{max}\right)$.

9: Return $\widehat{V}$ and ${\left\{I_{corr,k}\right\}}_{k=1}^N$.