In the compressive sensing reconstruction algorithm

the unknown sparsity and the fixed step-size are the factors that affect the reconstruction accuracy and running time of the algorithm.In view of the above shortcomings

we propose a regularized backtracking adaptive pursuit algorithm based variable step-size.Firstly

the sparsity of the signal is obtained by the way of atomic matching test.Then we combine the regularization method with the subspace tracking algorithm to achieve the second screening and remove the atoms which are not appropriate.Finally

we use a variable step-size to select atoms in the candidate set so that we can complete the signal reconstruction.The simulation results show that the proposed algorithm is superior to other algorithms in speed and reconstruction accuracy.