Overview
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.
Example
![](../../img/stone/original_2491.png)
![](../../img/stone/64x64_28.jpg)
![](../../img/stone/compressed_05percent_image_58.jpg)
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.