Thayer School, Dartmouth College.
|Parameter estimation in inverse problems is traditionally formulated as a least squares model fitting problem, with quadratic regularization. In the presence of outliers on the data, an in the context of ill-posed problems, the use of least squares approaches is particularly sensitive to data errors. Use of least absolute values fitting (1-norm on the data term) approaches is robust to presence of outliers and can produce meaningful results where least squares approaches fail. The use of the 1-norm is also interesting as an approach to regularization, leading to Total Variation regularization. This approach allows reconstructing parameters with much faster spatial variations compared to traditional quadratic regularization approaches. A Primal Dual Interior Point framework for the estimation of parameters in inverse problems using the 1-norm on the data and regularization terms will be discussed and practical application examples will be shown.|
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