Compressed　sensing　(CS)　theory　realizes　sparse　signal　sampling　at　a　sub-Nyquist　frequency　to　reduce　the　high　computational　cost　of　signal　processing　systems.　As　one　of　the　main　signal　processing　modules　of　the　CS　system,　the　signal　reconstruction　algorithm　determines　the　signal　processing　capability.　Although　orthogonal　matching　pursuit　(OMP)　is　conventionally　selected　in　hardware　implementations　for　its　low　complexity　and　high　regularity,　its　low　recovery　performance　is　still　a　problem.　In　this　paper,　based　on　the　projection-based　atom　selection　orthogonal　matching　pursuit　(POMP)　algorithm,　a　threshold　projection　orthogonal　matching　pursuit　(TPOMP)　algorithm　is　proposed　to　improve　the　reconstruction　accuracy　and　reduce　the　computational　complexity.　TPOMP　algorithm　expands　the　final　support　set　dynamically　and　in　parallel　by　setting　threshold　standards.　The　reconstruction　simulation　results　show　that　the　TPOMP　algorithm　exhibits　a　higher　reconstruction　success　rate　and　higher　reconstruction　efficiency　than　the　original　POMP.　The　proposed　reconstruction　processor　architecture　is　designed　and　implemented　using　Virtex　UltraScale+　HBM　VCU　128　FPGA　under　the　configuration　of　M　=　256,　N　=　1024　,　and　K　=　36.　The　reconstruction　results　show　that　the　proposed　processor　achieves　a　higher　reconstruction　signal-to-noise　ratio　(RSNR)　of　37.69　dB　with　18bits　data　width.　The　processor　can　run　at　a　clock　frequency　of　224.32　MHz　and　the　reconstruction　time　is　149.6　mu　s.