Algorithm 1: Blur Kernel Estimation Algorithm

Input: Blurred image$Y$ generate the initial value of each variable $\mathrm{for}i=1:5$ do $\epsilon \leftarrow {\epsilon }_0$  repeat  solve for $G$ using the gradient descent method, ${\gamma }^{\prime }\leftarrow 2\gamma ,{\mu }^{\prime }\leftarrow 2\mu$. repeat solve for $b$ using (26), solve for $c$ using (27), ${\rho }^{\prime }\leftarrow 2\rho$. repeat solve for $\tilde{X}$ using (21), ${\delta }^{\prime }\leftarrow 2\delta$. repeat solve for $a$ using (25),solve for $X$ using (31), ${\delta }^{\prime }\leftarrow 2\delta$. until ${\delta }^{\prime }>{\delta }_{max}^{\prime }$ ${\rho }^{\prime }\leftarrow 2{\rho }^{\prime }$. until ${\rho }^{\prime }>{\rho }_{max}^{\prime }$ ${\gamma }^{\prime }\leftarrow 2{\gamma }^{\prime },{\mu }^{\prime }\leftarrow 2{\mu }^{\prime }$. $\mathrm{until}{\gamma }^{\prime }>{\gamma }_{max}^{\prime }$ and ${\mu }^{\prime }>{\mu }_{max}^{\prime }$ $\epsilon \leftarrow 4\epsilon$.  until $\epsilon >{\epsilon }_{max}$  solve for $k$ using (34).  $\mu \leftarrow 0.9\mu ,\gamma \leftarrow 0.9\gamma ,\delta \leftarrow 0.9\delta$. end for Output: blur kernel$k$.