Data analysis tools for uncertainty quantification of inverse problems

We present exploratory data analysis methods to assess inversion estimates using examples based on l(2)- and l(1)-regularization. These methods can be used to reveal the presence of systematic errors such as bias and discretization effects, or to validate assumptions made on the statistical model used in the analysis. The methods include bounds on the performance of randomized estimators of a large matrix, confidence intervals and bounds for the bias, resampling methods for model validation and construction of training sets of functions with controlled local regularity.