An adaptive gradient greedy algorithm for compressed sensing

Greedy algorithm is powerful and practical and has been used frequently in compressed sensing because it leads to relatively small calculation and is easy to be realized. GraDeS (Gradient Descent with Sparsification) is one of the greedy algorithms, which reconstructs signal by gradient iteration with hard threshold. However the sparsity of original signal is necessary in GraDes which means it is only applicable to signals with known sparsity, but it is normally unreal in practice. This paper proposes an adaptive gradient greedy algorithm(AGraDeS) in which sparsity of signal is no more required. Experimental results show that the proposed algorithm reconstructs signal faster and precisely in most cases compared to some traditional algorithms, especially when the signal is big and with bad sparsity, this algorithm still performs better.