The sparseness adaptive matching pursuit algorithm (SAMP) is a classical algorithm based on
compressed sensing theory. Aiming at reconstructing signals with unknown sparsity, an adaptive step
forward-backward matching pursuit algorithm (AFBMP) is presented. The AFBMP select matching atoms in
the forward processing by using logarithmic variable steps which under the frame of sparseness adaptive
matching pursuit algorithm. At the beginning of iterations, high value of step size, causing fast convergence
of the algorithm is used to realize the coarse approach of signal sparse, and in the later smaller value of step
size is used to realize the precise reconstruction of the sparse signal which equal to half of the previous step.
Then AFBMP amend the mistakes which caused in the former stage and delete part of the false atoms in the
support set using the backward strategy. Finally it realizes the signal accurately approximate. Experiments
show that the AFBMP algorithm can reconstruct the unknown signal more efficiently.
