Acquiring deep-space images with high spatial resolution and sensitivity is important for space-debris surveillance and early warning. We propose a novel computational imaging (CI) method for high-sensitivity image acquisition in this letter. The proposed approach introduces CI into image formation. The proposed capturing process conducts minor modifications for cameras to encode more desirable information during capture, which is practical for hardware implementation. The latent image is reconstructed by formulating a recovery problem into an optimization problem, which is solved with iteratively reweighted least square technique. The experimental results clearly show the effectiveness of the proposed method.