A Greedy Sparse Approximation Algorithm Based On L1-Norm Selection Rules

We propose a new greedy sparse approximation algorithm, called SLS for Single L1 Selection, that addresses a least squares optimization problem under a cardinality constraint. The specificity and increased efficiency of SLS originate from the atom selection step, based on exploiting ℓ
₁
-norm solutions. At each iteration, the regularization path of a least-squares criterion penalized by the ℓ
₁
norm of the remaining variables is built. Then, the selected atom is chosen according to a scoring function defined over the solution path. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms when the solution is sparse.