The　Penalty　Decomposition　(PD)　method　is　an　effective　and　versatile　algorithm　for　sparse　optimization,　which　has　been　used　in　different　applications.　The　PD　method　may　be　slow,　since　it　needs　to　solve　many　subproblems.　The　accelerated　iteration　hard　thresholding　(AIHT)　method　is　also　a　powerful　method　for　sparse　optimization,　but　has　a　main　drawback　that　it　requires　a　prior　estimation　of　the　sparsity　level.　In　this　paper,　an　improvement　of　the　penalty　decomposition　method　is　proposed　for　the　sparse　optimization　problem,　which　embeds　the　AIHT　method　into　the　PD　method.　The　proposed　method　has　the　advantages　of　the　PD　method　and　the　AIHT　method,　but　avoids　their　disadvantages.　The　convergence　analysis　of　the　proposed　method　is　given　as　well.　Moreover,　computational　experiments　on　a　number　of　test　instances　demonstrate　the　effectiveness　of　the　proposed　method　in　accurately　generating　sparse　and　redundant　representations　of　one-dimensional　random　signals　and　two-dimensional　CT　images.　©　2015　Elsevier　B.V.