Algorithm 3 HOGS4 denoising engine using ADMM

Initialize: While ${\Vert \mathrm{PSNR}\left({\widehat{\mathbf{Z}}}^{\left(i+1\right)},{\mathbf{Z}}^{\left(j\right)}\right)-\mathrm{PSNR}\left({\widehat{\mathbf{Z}}}^{\left(i\right)},{\mathbf{Z}}^{\left(j\right)}\right)\Vert }_2^2>tol$ compute ${\widehat{\mathbf{Z}}}^{\left(i+1\right)}$ according to Equations (38)–(40); compute ${\mathbf{V}}^{\left(i+1\right)}$ according to Equations (41) and (42); compute ${\mathbf{W}}^{\left(i+1\right)}$ according to Equation (43); compute ${\mathbf{U}}_{vi}$ and ${\mathbf{U}}_{wi}$ according to Equation (44); End While Return ${\widehat{\mathbf{Z}}}^{\left(i+1\right)}$