Algorithm 1 Pseudo code for FFT operation-based data smoothing method

Input data: a Input parameter: μ Set parameter: ρ = 10, l = 100 Initialize ${\mathbf{f}}_0$ = 0, ${\mathbf{u}}_0$ = 0, ${\mathbf{y}}_0$ = 0 Compute the finite differences operator matrix $\mathbf{D}$ and its transpose ${\mathbf{D}}^T$ for i = 1:l 1. Solve $\mathbf{A}$ using Equation (5) 2. Solve $\mathbf{u}$ using Equation (6) 3. Update the Lagrange multiplier $\mathbf{y}$ using Equation (7) end