Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization by Jens Flemming

Author:Jens Flemming
Language: eng
Format: epub
ISBN: 9783319952642
Publisher: Springer International Publishing

Remember that F(x) = F(−x) for all x. The algorithm outputs only one of the two solutions. To improve presentation we manually flip the sign so that the signs of calculated and exact solution coincide.

We consider three examples. The table below shows the exact solution x †, the relative noise level δ rel, the number of iterations the algorithm performed until the discrepancy principle was satisfied and where to find corresponding plots.

We do not give extensive numerical results here. We only demonstrate with few examples that the described method works well and discuss a number of features the reconstructions show. The interested reader finds further numerical experiments and a comparison to other methods in [49].

Figure 6.2 shows the exact solution x † for example 1. Figures 6.3 and 6.4 show corresponding exact and noisy data. The output of the algorithm is depicted in Fig. 6.5. For better comparability real and imaginary parts are plotted in Figs. 6.6 and 6.7 for exact and noisy data and in Figs. 6.8 and 6.9 for exact and reconstructed solution. The same system is used for the figures belonging to examples 2 and 3.

Fig. 6.2Exact solution for example 1

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