Recovery of cosparse signals with Greedy Analysis Pursuit in the presence of noise

The sparse synthesis signal model has enjoyed much success and popularity in the recent decade. Much progress ranging from clear theoretical foundations to appealing applications has been made in this field. Alongside the synthesis approach, an analysis counterpart has been used over the years. Despite the similarity, markedly different nature of the two approaches has been observed. In a recent work, the analysis model was formally formulated and the nature of the model was discussed extensively. Furthermore, a new greedy algorithm (GAP) for recovering the signals satisfying the model was proposed and its effectiveness was demonstrated. While the understanding of the analysis model and the new algorithm has been broadened, the stability and the robustness against noise of the model and the algorithm have been mostly left out. In this work, we adapt and propose a new GAP algorithm in order to deal with the presence of noise. Empirical evidence for the algorithm is also provided.