  A major threat to satellites is space debris with their low mass and high
rotational speed. Accordingly, the short observation time of these objects is a
major limitation in space research for appropriate detection and decision. As a
result, these objects do not fully illuminated, leading to their incomplete
images at any snapshot. In this paper, we propose a method to decrease the
number of snapshots in a given observation time and using a limited number of
spot beams per snapshot called 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 T V norm is more
appropriate. We develop a procedure to recover space debris and satellites
using L1 and T V norms. Using simulation results, we compare the results with
the well-known SBL and SL0 norm in terms of the number of snapshots, MSE, SNR,
and running time. It is shown that our proposed method can successfully recover
the space objects images using a fewer number of snapshots.
