The STONE Transform: Multi-Resolution Image Enhancement and Real-Time Compressive Video

This is an interesting direction especially coming from some of the inventors of the single pixel camera. The following paper does compressive sensing on images and video but it does so by allowing what they call a preview capability, i.e. the ability to produce, with very little computation, a low resolution image without the complexity required to go faster than a blink of an eye. This is significant in two ways:

• the way the measurement matrix is designed opens the door to numerous different implementations
• the approach provides a way for hybrid systems and more importantly lends credence to the work on infinite dimensional work/generalized sampling which points to a requirement to sample 'normally' in the low frequency range (which is what those previews are).

without further due here is the paper:

The STONE Transform: Multi-Resolution Image Enhancement and Real-Time Compressive Video by Tom Goldstein, Lina Xu, Kevin F. Kelly, Richard Baraniuk

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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