Dirk A. Lorenz

TL;DR: The linearized Bregman method is a method to calculate sparse solutions to systems of linear equations as mentioned in this paper, which is a special case of the linearized bregman algorithm.

TL;DR: In this paper, the uncertainty principle in the context of the ane-w eyl-Heisenberg group in one and two dimensions is considered. But the minimizers obtained for these sections actually interpolate between Gabor and wavelets functions.

TL;DR: In this article, a unified approach to iterative soft thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented, and a new convergence analysis is presented.

Abstract: This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact—a situation we refer to as “mismatched adjoint”. We show that the method may still converge both in the over- and underdetermined consistent case under appropriate conditions, and we calculate the expected asymptotic rate of linear convergence. Moreover, we analyze the inconsistent case and obtain results for the method with mismatched adjoint as for the standard method. Finally, we derive a method to compute optimized probabilities for the choice of the rows and illustrate our findings with numerical examples.

TL;DR: In this article, a subgradient method for the minimization of nonsmooth convex functions over a convex set is proposed, where adaptive approximate projections only require to move within a certain distance of the exact projections (which decreases in the course of the algorithm).