# Parameter Identification Problems with Uniform Noise

Christian Clason^{*}

For inverse problems where the data is corrupted by uniform noise, it is well-known that the $\text{L}^\infty$ norm is a more robust data fitting term than the standard $\text{L}^2$ norm. Such noise can be used as a statistical model of quantization errors appearing in digital data acquisition and processing. However, the numerical solution is challenging due to the nondifferentiability of the Tikhonov functional. Using an equivalent formulation, it is possible to derive optimality conditions that are amenable to numerical solution by a superlinearly convergent semi-smooth Newton method. The automatic choice of the regularization parameter using a simple fixed-point iteration is also addressed. Numerical examples illustrate the performance of the proposed approach as well as the qualitative behavior of $\text{L}^\infty$ fitting for coefficient inverse problems.

Mathematics Subject Classification: 65M32

Keywords: inverse problem; parameter identification; non-Gaussian noise; semismooth Newton

Minisymposion: Dual Methods for Approaching Inverse Problems