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In this letter, we apply a new sampling theory named compressed sensing (CS) for aerospace remote sensing to reduce data acquisition and imaging cost. We can only record directly single or multiple pixels while need not the use of additional compression step to improve the problems of power consumption, data storage, and transmission, without degrading spatial resolution and quality of pictures. The CS remote sensing includes two steps: encoding imaging and decoding recovery. A noiselet-transform-based single-pixel imaging and a random Fourier-sampling-based multipixel imaging are alternatively used for encoding, and an iterative curvelet thresholding method is used for decoding. The new sensing mechanism shifts onboard imaging cost to offline decoding recovery. It would lead to new instruments with less storage space, less power consumption, and smaller size than currently used charged coupled device cameras, which would match effective needs particularly for probes sent very far away. Numerical experiments on potential applications for Chinese Chang'e-1 lunar probe are presented.