Smoothing and Regularization with Modified Sparse Approximate Inverses

Figure 6

Reconstruction error against the iteration for the 2D problem with blur operator 𝐻⁴² and original data 𝑥₁ of size 𝑛=50² affected by random noise of order 0.1%. CG is compared to CG for the normal equations and to 𝑀5_𝜌 (a) and MSPAI satisfying 𝜌𝑅5_𝐺1 (b), respectively.

(a) PCG using the optimal preconditioner 𝑀5_𝜌(51)

(b) PCG using MSPAI satisfying 𝜌𝑅5_𝐺1