Sparsity-Enabled Step Width Adaption for Linearized Bregman based Algorithms

Iterative algorithms based on linearized Bregman iterations allow efficiently solving sparse estimation problems. Especially the Kaczmarz and sparse least mean squares filter (LMS) variants are very suitable for implementation in digital hard- and software. However, when analyzing the error of such algorithms over the iterations one realizes that especially at early iterations only small error reductions occur. To im- prove this behavior, we propose to use sparsity-enabled step width adaption. We show simulations results demonstrating that this approach significantly improves the performance of sparse Kaczmarz and sparse LMS algorithms.