A new blind sparsity iterative greedy reconstruction algorithm is presented based on studying the signal reconstruction algorithm for compressed sensing without the prior information of signal sparsity.A stage-wised and backtracking method is employed to adaptively adjust the candidate list at each iteration in order to estimate the true supporting set of the approximated signal.The theoretical analysis and experiment simulation prove that the performance of the algorithm outperforms that of the existing state-of-art iterative greedy matching pursuit algorithms

and provides a generalized greedy reconstruction framework.The orthogonal matching pursuit and subspace pursuit can be viewed as its special case

and it also gives the best trade-offs between computational complexity and reconstruction performance.This makes it a promising candidate for many practical applications for compressed sensing signal reconstruction.