  In this paper we propose three iterative greedy algorithms for compressed
sensing, called \emph{iterative alternating direction} (IAD), \emph{normalized
iterative alternating direction} (NIAD) and \emph{alternating direction
pursuit} (ADP), which stem from the iteration steps of alternating direction
method of multiplier (ADMM) for $\ell_0$-regularized least squares
($\ell_0$-LS) and can be considered as the alternating direction versions of
the well-known iterative hard thresholding (IHT), normalized iterative hard
thresholding (NIHT) and hard thresholding pursuit (HTP) respectively. Firstly,
relative to the general iteration steps of ADMM, the proposed algorithms have
no splitting or dual variables in iterations and thus the dependence of the
current approximation on past iterations is direct. Secondly, provable
theoretical guarantees are provided in terms of restricted isometry property,
which is the first theoretical guarantee of ADMM for $\ell_0$-LS to the best of
our knowledge. Finally, they outperform the corresponding IHT, NIHT and HTP
greatly when reconstructing both constant amplitude signals with random signs
(CARS signals) and Gaussian signals.
