Compressed 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.
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