Scaled Linearized Bregman Iterations for Fixed Point Implementation

The estimation of sparse vectors is an important problem in digital signal processing. Recently, efficient iterative algorithms based on the so-called linearized Bregman iterations have been proposed, combining excellent estimation performance with low implementation complexity. Unfortunately, these algorithms typically use large numerical values, complicating fixed point implementations. To overcome this problem, we propose a modification of these algorithms based on scaling at specific algorithmic steps. We show that with this modification the algorithm still converges to the optimal solution and that it allows to implement linearized Bregman iterations completely in fractional precision fixed point. We show bit true simulation results, as well as synthesis results demonstrating the performance of the implemented algorithms.