Algorithm 1: Solving sparse representation coefficients $\mathbf{A}$.

Input: The templates set $\mathbf{D}$, the candidate samples $\mathbf{Y}$ and the Lipschitz constant ξ. 1: The initial value of optimal solution: ${\mathbf{A}}_0={\mathbf{A}}_{-1}=\mathbf{0}$, iteration parameter: ${\varsigma }_0={\varsigma }_{-1}=1$. 2: Calculating the following expressions, $k=0,1,\dots$, not until convergence. $\left\{\begin{array}{c}{\mathbf{M}}_{k+1}={\mathbf{A}}_k+\frac{{\varsigma }_{k-1}-1}{{\varsigma }_k}({\mathbf{A}}_k-{\mathbf{A}}_{k-1})\hfill \\ {\varsigma }_{k+1}=\frac{1+\sqrt{1+4{\varsigma }_k^2}}{2}\hfill \\ {\mathbf{A}}_{k+1}=arg\underset{\mathbf{A}}{min}\frac{\xi }{2}{∥\mathbf{A}-{\mathbf{M}}_{k+1}+\frac{\nabla F\left({\mathbf{M}}_{k+1}\right)}{\xi }∥}_2^2+G\left(\mathbf{A}\right)\hfill \end{array}\right.$ Output: The calculated sparse representation coefficients $\widehat{\mathbf{A}}$.