Many research fields have the motivation using the compressive sensing. All the CS problems pursue the high speed (low complexity) and high signal reconstruction per- formance. This study proposed a projection-based atom selection orthogonal matching pursuit (POMP) with multiple candidates and matrix inversion bypass (MCMIB) al- gorithm. The POMP has better signal-to-noise ratio (SRNR) performance than the orthogonal matching pursuit (OMP) algorithm, but the computational complexity of the POMP is extremely high. This algorithm greatly simplified the computational com- plexity of the POMP algorithm without loss any SRNR performance. The architecture is designed for the 256-length input vector with sparsity 12, and 64 measurement data. The proposed processor is implemented by TSMC 90nm 1P9M CMOS technology. The clock frequency is 140MHz, and the chip area is 11.18mm 2 . The total reconstruction time is 72.25 µs.