Sparse Regularization-Based Reconstruction for Bioluminescence Tomography Using a Multilevel Adaptive Finite Element Method

Algorithm 2

Multilevel 𝑙₁-regularized reconstruction algorithm.

Initialize the parameter: set 𝑘_max=4, 𝜀=1e−6, 𝜂=0.2, set the initial PSR;

𝑘=1, discretize the model into a uniformly tetrahedral-element mesh;

Establish the linear system equation 𝐴₁𝑆₁=Φ^𝑚1, and solve it with TNIPM;

While  𝑘<𝑘_max 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 𝑘th mesh level;

End while