T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, "The STOne Transform: Multi-Resolution Image Enhancement and Real-Time Compressive Video," 2013.

Abstract:  Compressive sensing enables the reconstruction of high-resolution signals from under-sampled data. While compressive methods simplify data acquisition, they require the solution of difficult recovery problems to make use of the resulting measurements. This article presents a new sensing framework that combines the advantages of both conventional and compressive sensing. Using the proposed STOne transform, measurements can be reconstructed instantly at Nyquist rates at any power-of-two resolution. The same data can then be “enhanced” to higher resolutions using compressive methods that leverage sparsity to “beat” the Nyquist limit. The availability of a fast direct reconstruction enables compressive measurements to be processed on small embedded devices. We demonstrate this by constructing a real-time compressive video camera.

(a)                                      (b)                                      (c)                                     (d)

The above example demonstrates reconstruction of high speed video from under-sampled measurements.  (a) 256x256 image frame from a video acquired at full resolution. (b) 64x64 image frame directly reconstructed from STOne measurements at a rate 6.25% of the full-rate measurements. (c) 256x256 image frame recovered from STOne measurements at a rate 5% of the full-rate measurements. (d) 256x256 image frame recovered from STOne measurements at a rate 1% of the full-rate measurements.