Deblurring from highly incomplete measurements for remote sensing

When we take photos, we often get blurred pictures because of hand shake, motion, insufficient light, unsuited focal length, or other disturbances. Recently, a compressed-sensing (CS) theorem which provides a new sampling theory for data acquisition has been applied for medical and astronomic imaging. The CS makes it possible to take superresolution photos using only one or a few pixels, rather than million pixels, with a conventional digital camera. Here, we further consider a so-called CS deblurring problem: Can we still obtain clear pictures from highly incomplete measurements when blurring disturbances occur? A decoding algorithm based on Poisson singular integral and iterative curvelet thresholding is proposed to correct the deblurring problem with surprisingly incomplete measurements. It permits one to design robust and practical compressed-imaging instruments involving less imaging time, less storage space, less power consumption, smaller size, and cheaper than currently used charged coupled device cameras, which effectively match the needs, particularly for probes sent very far away. It essentially shifts the onboard imaging cost to an offline recovery computational cost. Potential applications in aerospace remote sensing of the Chinese Chang'e-1 lunar probe are presented.