Rapid Convergence of Image Reconstruction

Example 5

When an iterative image reconstruction algorithm converges quickly, reconstructed images can be provided for on-site diagnosis by physicians. To compare the convergence of different reconstruction methods, the Least Square Error (LSE), ∥U_sc−WX∥² for each method was normalized to the power of the scattered field, ∥U^sc∥², which served as the initial objective function for unregularized CG method. Shown in FIG. 15 are the mean and standard deviations of normalized LSE for the five methods using phantom data. Truncated pseudoinverse provided a good initial guess which reduced the initial LSE, ∥U_sc−WX∥², to 4% of the power of the scattered field, ∥U_sc∥². Newton and CG with PINV as an initial estimate converged in 1 and 2 iterations, respectively. Newton and CG with zero initial converged in 1 and 3 iterations, respectively, and the residual LSE of CG was slightly higher than that with PINV as an initial. Unregularized CG converged in 3 iterations.