Super-resolution imager via compressive sensing

In this paper, we propose a novel imager that can acquire super-resolution (SR) images with significantly fewer sensors. The theoretical basis of this imager is compressive sensing (CS) theory, which calls for a measurement matrix with good properties for effective reconstruction, such as RIP. Such a property indicates that entries of the received signal are effectively aliased. In our imager we use an optic effect called spherical aberration to achieve such aliased measurement of light intensity (the signal), thus realizing an ideal measurement matrix. The original image can then be efficiently reconstructed through the Alternating Direction Method (ADM). The implementation of the proposed imager needs only replace an ordinary lens with a spherical lens of large curvature, with almost no additional cost, in contrast with existing complex systems, such as the single pixel camera using the micro-mirror device. Simulation results show that despite its simplicity, the performance of the proposed imager is comparable with traditional CS models (most of which are difficult for physical implementation). Further, since the lens is a linear shift-invariant (LSI) system, FFT can be incorporated into the ADM algorithm to accelerate the reconstruction, adding to its advantage over some other CS-based imagers.