The approximation of a signal using a limited number of dictionary elements is stated as an L0-constrained or an L0-penalized least-square problem. We first give the working assumptions and then propose the heuristic Single Best Replacement (SBR) algorithm for the penalized problem. It is inspired by the Single Most Likely Replacement (SMLR) algorithm, initially proposed in the context of Bernoulli-Gaussian deconvolution. Then, we extend the SBR algorithm to a continuation version estimating a whole solution path, i.e., a series of solutions depending on the level of sparsity. The continuation algorithm, up to a slight adaptation, also provides an estimate of a solution path of the L0-constrained problem. The effectiveness of this approach is illustrated on a sparse signal deconvolution problem.