International Journal of Biomedical Imaging / 2011 / Article / Alg 2

Research Article

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

Algorithm 2

Multilevel 𝑙 1 -regularized reconstruction algorithm.
Initialize the parameter: set π‘˜ m a x = 4 , πœ€ = 1 e βˆ’ 6 , πœ‚ = 0 . 2 , set the initial PSR;
π‘˜ = 1 , discretize the model into a uniformly tetrahedral-element mesh;
Establish the linear system equation 𝐴 1 𝑆 1 = Ξ¦ π‘š 1 , and solve it with TNIPM;
While   π‘˜ < π‘˜ m a x and | Ξ¦ 𝑐 βˆ’ Ξ¦ π‘š | > πœ€
 Select those elements satisfy 𝑠 𝑖 > πœ‚ β€– 𝑆 β€– ∞ 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 π‘˜ th mesh level;
End while