We propose and demonstrate a compressive sensing (CS) framework for correlation holography. This is accomplished by adopting the principle of compressive sensing and thresholding in the two-point intensity correlation. The measurement matrix and the sensing matrix that are required for applying the CS framework here are systematically extracted from the random illuminations of the laser speckle data. Reconstruction results using CS, CS with thresholding, and intensity correlation are compared. Our study reveals that liminal CS requires far fewer samples for the reconstruction of the hologram and has wide application in image reconstruction. © 2017 Optical Society of America.