In this correspondence, we introduce a new imaging method to obtain high-resolution (HR) images. The image acquisition is performed in two stages, compressive measurement and optimization reconstruction. In order to reconstruct HR images by a small number of sensors, compressive measurements are made. Specifically, compressive measurements are made by a low-resolution (LR) camera with randomly fluttering shutter, which can be viewed as a moving random exposure pattern. In the optimization reconstruction stage, the HR image is computed by different models according to the prior knowledge of scenes. The proposed imaging method offers a new way of acquiring HR images of essentially static scenes when the camera resolution is limited by severe constraints such as cost, battery capacity, memory space, transmission bandwidth, etc. and when the prior knowledge of scenes is available. The simulation results demonstrate the effectiveness of the proposed imaging method.