Compressed　sensing　(CS)　avoids　the　limitation　of　the　Nyquist　sampling　theorem　on　sampling　rate,　it　allows　to　reconstruct　sparse　signals　sampled　at　a　sub-Nyquist　frequency.　In　this　paper,　based　on　the　orthogonal　matching　pursuit　(OMP)　algorithm,　a　high　critical　sparsity　orthogonal　matching　pursuit　(HCSOMP)　algorithm　is　proposed　to　improve　the　recovery　performance.　The　HCSOMP　algorithm　achieves　more　accurate　reconstruction　performance　through　the　combination　of　extended　potential　support　set　and　backtracking　strategy.　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　architecture　achieves　a　signal-to-reconstruction-noise　ratio　(SRNR)　of　21.21　dB　and　runs　at　a　clock　frequency　of　198.4　MHz　with　a　reconstruction　time　of　360.4　μs.　©　2023　IEEE.