  We develop a primal dual active set with continuation algorithm for solving
the \ell^0-regularized least-squares problem that frequently arises in
compressed sensing. The algorithm couples the the primal dual active set method
with a continuation strategy on the regularization parameter. At each inner
iteration, it first identifies the active set from both primal and dual
variables, and then updates the primal variable by solving a (typically small)
least-squares problem defined on the active set, from which the dual variable
can be updated explicitly. Under certain conditions on the sensing matrix,
i.e., mutual incoherence property or restricted isometry property, and the
noise level, the finite step global convergence of the algorithm is
established. Extensive numerical examples are presented to illustrate the
efficiency and accuracy of the algorithm and the convergence analysis.
