Initialize the parameter: set 𝑘 m a x = 4 , 𝜀 = 1 e 6 , 𝜂 = 0 . 2 , set the initial PSR;
𝑘 = 1 , discretize the model into a uniformly tetrahedral-element mesh;
Establish the linear system equation 𝐴 1 𝑆 1 = Φ 𝑚 1 , and solve it with TNIPM;
While   𝑘 < 𝑘 m a x and | Φ 𝑐 Φ 𝑚 | > 𝜀
 Select those elements satisfy 𝑠 𝑖 > 𝜂 𝑆 to form the new PSR based on the solution at current
 mesh level;
 Perform local mesh refinement and interpolate the new PSR to the next finer mesh;
k++; Form and solve the new system equation with TNIPM at the 𝑘 th mesh level;
End while
Algorithm 2: Multilevel 𝑙 1 -regularized reconstruction algorithm.