Abstract:

As the existing orthogonal matching pursuit （OMP） algorithms acquire the reconstruction with given number of iterations, i.e. given sparsity level of the image to be reconstructed, many linear measurements are needed to ensure the reconstruction accuracy. In order to reduce the number of linear measurements, an improved backward-optimized OMP algorithm is presented, in which an optimized orthogonal matching pursuit （OOMP） algorithm is adopted to restrict the selection of atoms based on the optimized orthogonality in the iteration process, thus optimizing the selection of atoms with a minimum current residual error. The sparsity level is then taken as the standard of the adaptive iteration number, and a very simple principle of atom selection is proposed to post-process the iteration results, thus backward eliminating the superfluous atoms and acquiring exact reconstruction. Simulated and experimental results indicate that, as compared with the existing OMP algorithms, the proposed algorithm helps to acquire the reconstruction with higher accuracy and fewer measurements.

Key words: image reconstruction, orthogonal matching pursuit, compressible sensing, residual error