Regularized sequential selection and backtracking removal for CS atom matching

Atom selection is crucial to compressive sensing (CS) reconstruction by orthogonal matching pursuit (OMP), where the look-ahead (LA) OMP algorithm (LAOMP) evaluated final effects of all the LA atoms before they were included into a support set, certainly, a high computation burden has to be suffered. This paper modifies LAOMP method by two folds: 1) Regularization (R-LAOMP) is introduced to restrict the atom selection by similar small residuals, while mutual effects of new selected atoms are considered to alleviate the high computation costs. 2) Backtracking-based (LA-BOMP) atom pruning is employed to remove the most mismatching atoms in support sets to balance the accuracy and the random disturbance in optimization procedures. Accordingly this regularized forward atom evaluation combining backward atom deleting method (R-LA-BOMP) leads to a significant improvement in LAOMP, while a trade-off between performance and complexity is achieved. Experiments of the regularized atom selection and the backtracking pruning algorithms are performed on Gaussian sparse signals, 0-1 sparse signals and speech voices and the results are given.