  We propose an efficient algorithm for sparse signal reconstruction problems.
The proposed algorithm is an augmented Lagrangian method based on the dual
sparse reconstruction problem. It is efficient when the number of unknown
variables is much larger than the number of observations because of the dual
formulation. Moreover, the primal variable is explicitly updated and the
sparsity in the solution is exploited. Numerical comparison with the
state-of-the-art algorithms shows that the proposed algorithm is favorable when
the design matrix is poorly conditioned or dense and very large.
