General regularization framework for DEER spectroscopy.

Tikhonov regularization is the standard processing technique for the inversion of double electron-electron resonance (DEER) data to distance distributions without assuming a parametrized model. In other fields it has been surpassed by modern regularization methods. We analyze such alternative regularization methods based on the Tikhonov, total variation (TV) and Huber penalties with and without the use of Bregman iterations. For this, we provide a general mathematical framework and its open-source software implementation. We extend an earlier approach by Edwards and Stoll for the selection of an optimal regularization parameter to all of these penalties and use their big test data set of noisy DEER traces with known ground truth for assessment. The results indicate that regularization methods based on Bregman iterations provide an improvement upon Tikhonov regularization in recognizing features and recovering distribution width at moderate signal-to-noise ratio, provided that noise variance is known. Bregman-iterative methods are robust with respect to the method used in the choice of regularization parameter.