Backtracking Regularized Adaptive Matching Pursuit Algorithm for Signal Reconstruction of Compressive Sampling

Regularized orthogonal matching pursuit algorithm is a widely used reconstruction algorithm for compressive sampling, but it needs the sparsity of signal as a precondition. In order to overcome this disadvantage, a backtracking regularized adaptive matching pursuit algorithm is proposed, which aims at reconstructing the original signal when the sparsity is unknown. This algorithm is based on the regularized orthogonal matching pursuit algorithm. At beginning, fuzzy threshold is set for atoms selection, then the regularization processing is used to filter them. At last, some wrong atoms is deleted by using the backtracking method. The support set is updated while it is being enlarged gradually in every iteration, so it can approximate the sparsity of signal. Under the same condition, compared with the other greedy algorithms, the experimental results show that the superior reconstruction performance of the proposed algorithm for 1D sparse signal and 2D images and the running time is modest.