Detection followed by projection in conventional privacy cameras is vulnerable to software attacks that threaten to expose image sensor data. By multiplexing the incoming light with a coded mask, a FlatCam camera removes the spatial correlation and captures visually protected images. However, FlatCam imaging suffers from poor reconstruction quality and pays no attention to the privacy of visual information. In this paper, we propose a deep learning-based compressive sensing approach to reconstruct and protect sensitive regions from secured FlatCam measurements. We predict sensitive regions via facial segmentation and separate them from the captured measurements. Our deep compressive sensing network was trained with simulated data, and was tested on both simulated and real FlatCam data.