92mm	Summary of schemes for Beltrami regularization
$$\text{gradient\hspace{0.17em}descent\hspace{0.17em}}\{\begin{array}{l}\Delta u^n=-\Delta t\left(\lambda K^T*K*\left(u^n-g\right)-D_{\beta ,\Delta x}^2{u}^n\right)\hfill \\ \Delta t\le \Delta x^2\left(\frac{2}{4N\beta +\lambda \Delta x^2}\right)\hfill \end{array}$$ (53)
$$\text{1-order\hspace{0.17em}accelerated}\{\begin{array}{l}\Delta u^n=\frac{1}{1+a\Delta t}\Delta u^{n-1}-\frac{\Delta t^2}{1+a\Delta t}\left(\lambda K^T*K*\left(u^n-g\right)-D_{\beta ,\Delta x}^2{u}^n\right)\hfill \\ \Delta t\le \Delta x\left(\sqrt{\frac{4}{4N\beta +\lambda \Delta x^2}+{\left(\frac{a\Delta x}{4N\beta +\lambda \Delta x^2}\right)}^2}+\frac{a\Delta x}{4N\beta +\lambda \Delta x^2}\right)\hfill \end{array}$$ (54)
$$\text{2-order\hspace{0.17em}accelerated\hspace{0.17em}}\{\begin{array}{l}\Delta u^n=\frac{2-a\Delta t}{2+a\Delta t}\Delta u^{n-1}-\frac{2\Delta t^2}{2+a\Delta t}\left(\lambda K^T*K*\left(u^n-g\right)-D_{\beta ,\Delta x}^2{u}^n\right)\hfill \\ \Delta t\le \Delta x\left(\frac{2}{\sqrt{4N\beta +\lambda \Delta x^2}}\right)\hfill \end{array}$$ (55)
$$\text{\hspace{0.17em}semi-implicit\hspace{0.17em}}\{\begin{array}{l}{v}^n=u^n+\frac{2-a\Delta t}{2+a\Delta t}\Delta u^{n-1}\hfill \\ u^{n+1}=v^n-\frac{2\Delta t^2}{2+a\Delta t}\left(\lambda K^T*K*\left(v^n-g\right)-D_{\beta ,\Delta x}^2{v}^n\right)\hfill \\ \Delta t\le \Delta x\left(\frac{2}{\sqrt{3\left(4N\beta +\lambda \Delta x^2\right)}}\right)\hfill \end{array}$$ (56)