Algorithm 1. The solving process of the proposed method.

INPUT:  $K$: the maximum number of iterations;  $tol$: the tolerance parameter. $\mathrm{INIT}:\rho =\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$L$}\right.,t^1=1,X^0=r^1=0,k=0;$ OUTPUT:   $\widehat{X}$: the reconstructed diffusion weighted (DW) images.

REPEAT: $$\begin{array}{l}k=k+1;\\ x_g=r^k-\rho \nabla f\left(r^k\right);\\ X^k=pro{x}_{\rho }\left(\alpha {\Vert X\Vert }_{*}\right)\left(x_g\right);\\ t^{k+1}=\frac{1+\sqrt{1+4{\left(t^k\right)}^2}}{2};\\ r^{k+1}=X^k+\frac{t^{k-1}-1}{t^k}\left(X^k-X^{k-1}\right);\end{array}$$ $\mathbf{UNTIL}k>K$$\mathbf{OR}\frac{{\Vert X^{k-1}-X^k\Vert }_2}{{\Vert X^k\Vert }_2}<tol$.