Algorithm 1.

The framework of TTV algorithm.

Input: Regularization parameters γi, i = t, x, y, z

Output: Flow-scaled residue functions K ∈ ℝT × N1 × N2 × N3.

K0 = 0

t1 = r1 = K0

for n = 1, 2, …, N do Steepest gradient descent $$K_g=r^n+s^{n+1}{A}^T(C-A{r}^n)$$ where $s^{n+1}=\frac{\mathit{\text{vec}}{(Q)}^T\mathit{\text{vec}}(Q)}{\mathit{\text{vec}}{(AQ)}^T\mathit{\text{vec}}(AQ)}$, Q ≡ AT (Arn − C) Proximal map: $$K^n={\text{prox}}_{\gamma }(2{\Vert K\Vert }_{TV})({\mathit{\text{fold}}}_t(K_g))$$ where ${\text{prox}}_{\rho }(g)(x)≔\underset{u}{\text{arg min }}\{g(u)+\frac{1}{2\rho }{\Vert u-x\Vert }^2\}$ Update t, r $$t^{n+1}=(1+\sqrt{1+4{(t^n)}^2})/2$$ $$r^{n+1}=K^n+((t^n-1)/t^{n+1})(K^n-K^{n-1})$$

end for