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A major threat to satellites is space debris, which are observed in orbit for a short time due to their low mass and high rotational speed. This major limitation causes them not to be fully illuminated in one snapshot, resulting in their incomplete image reconstruction and identification. In this paper, we propose a method to decrease the number of snapshots in a given observation time and use a limited number of spot beams per snapshot, which we call the encoded aperture. To recover the space debris images, an inverse problem is defined based on compressive sensing methods. Also, we show that for satellite imaging the Total Variation (TV) norm is more appropriate. We develop a procedure to recover space debris and satellites using L 1 and TV norms. Using simulation results, the proposed method is compared with the well-known Sparse Bayesian Learning (SBL) and S L 0 methods in terms of the number of snapshots, minimum Mean Square Error (MSE), Signal-to-Noise Ratio (SNR), and running time. It is shown that the proposed method can successfully recover the images of space objects using a fewer number of snapshots. [ABSTRACT FROM AUTHOR]