The stone transform: flexible compressed sensing


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. The stone transform is 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.


Reconstruction of a low resolution preview. The original image is measured in the transform domain where the stone coefficients are sub-sampled. The sub-sampled coefficients are then re-binned into a low resolution stone domain where the measurements are complete. Finally, the low-resolution transform is inverted to obtain the preview. By reinterpreting under-sampled data as fully-sampled data at a lower resolution, the stone transform allows "instant" reconstruction from compressive measurements. Alternatively, compressed sensing methods can be used to reconstruct at the original (high) resolution.



Reconstruction of high speed video from under-sampled data. (left) A frame from the original full resolution video. (center) A 64x64 preview generated from a stream with 6.25% sampling. (right) Compressive reconstructions using 6.25% sampling.

SUNets perform extremely well on semantic segmentation tasks (top 2 on PASCAL VOC challenge) using a small number of parameters and a simple portable architecture. SUNets also train relatively fast and with relatively low memory requirements, making them a practical choice as a component in more complex systems.

Stone transform resources

The paper describing the stone transform is available here:

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

A Matlab implementation of the stone transform, and code to replicate the experiments in this paper, is available via github.

The stone github page