Correlation imaging is an innovative imaging scheme, which transforms the imaging time to a spatial resolution by a single pixel detector. However, there are problems of low reconstruction quality and long data acquisition time. Hadamard coded modulation computation correlation imaging can achieve efficient imaging and significantly improve the applicability, but the noise in imaging reconstruction, which restricted the practicability, is a challenge needs to be tackled urgently. A correlation imaging related noise suppression scheme was proposed by thresholding method and morphological image enhancement, by analyzing the noise characteristics of the reconstructed results of the correlation imaging, which the Hadamard matrix as a measurement matrix and the feasibility of this scheme was verified by experiments, and nearly 8 dB enhancement of optical image was achieved. This imaging scheme is efficient for two valued images and grayscale images, and its work promotes the practicability of correlation imaging technology.