FROGS: A serial reversible greedy search algorithm

For compressed sensing, in the framework of greedy search reconstruction algorithms, we introduce the notion of initial support-set. The initial support-set is an estimate given to a reconstruction algorithm to improve the performance of the reconstruction. Furthermore, we classify existing greedy search algorithms as being serial or parallel. Based on this classification and the goal of robustness to errors in the initial support-sets we develop a new greedy search algorithm called FROGS. We end the paper with careful numerical experiments concluding that FROGS perform well compared to existing algorithms (both in terms of performance and execution time) and that it is robust against errors in the initial support-set.