The　orthogonal　matching　pursuit　(OMP)　has　been　widely　explored　to　realize　real-time　compressed　sensing　(CS)　reconstruction.　The　matrix　pseudo-inverse　of　the　least　squares　(LSs)　is　the　most　computationally　complex　operation　in　the　OMP.　Among　various　algorithms　to　realize　this　complex　operation,　the　alternative　Cholesky　decomposition　(ACD)　algorithm　performs　the　best.　However,　it　typically　involves　a　very　long　computation　time　due　to　its　iterative　procedure.　To　accelerate　the　ACD-OMP　algorithm,　a　novel　method　called　clustered　computing　look-ahead　(CCL)　is　proposed.　Inspired　by　the　famous　parallel　carry　look-ahead　adder　(CLA),　CCL　adds　a　propagation　matrix　to　decouple　the　data　dependency　in　ACD　and　then　uses　a　clustering　operator　to　transform　the　iterative　computation　of　ACD　into　a　pipelined　and　parallelized　computation.　This　brief　also　proposes　an　efficient　hardware　architecture　of　the　CCL-based　ACD-OMP　algorithm　for　CS　reconstruction.　The　proposed　algorithm　is　implemented　on　field　programmable　gate　array　(FPGA).　For　sparse　signals　with　the　same　sparsity　and　length,　the　proposed　implementation　is　1.96　times　faster　than　state-of-the-art　work.