Selection order framework algorithm for compressed sensing

The framework improves the performance of greedy algorithms.The framework only needs the selection orders of atoms of the parent algorithm.The framework is very simple in both the computational complexity and the actual operation. Greedy algorithms, which employ iterative greed strategy, are applied widely due to fast speed and simple structure. However, the reconstruction accuracy of greedy algorithm has a lot of room for improvement. To alleviate this drawback, an improved framework, called selection order framework, is proposed in this paper. This framework is very useful for greedy algorithms which use the correlation between columns of measurement matrix and the residue to select atoms per iteration. Moreover, to improve the recovery accuracy, the proposed framework only needs the selection order of atoms in estimated support set, which is available in original algorithm. The proposed framework also provides an adjustable parameter to control the tradeoff between the reconstruction accuracy and the run time. The efficiency of the proposed framework is demonstrated by simulations using sparse signals and a sparse image.