Table 1 Complete description of our proposed algorithm

Input: the Fourier magnitude b;

Initialization: t = 1, initial estimated image x ⁽⁰⁾, error tolerance τ > 0, parameters λ, γ, ρ ₁, ρ ₂

Repeat

Update image x ^(t) by (14);

Update z ^(t), y ^(t) by (20) and (22), respectively;

Update the scaled dual variables \( {\mathbf{u}}_1^{(t)} \), \( {\mathbf{u}}_2^{(t)} \) by (23);

t = t + 1;

Until maximum iteration number is reached or res ≤ τ

Output: final estimated image