Overview

This repository implements the stone transform, and accompanying demos, for compressive sensing and reconstruction of video. The implementation is in Matlab, with compilable C-langauge "mex" components. The STOne transform and its applications are described here: https://arxiv.org/abs/1311.3405.

To get started, run the setupSTO.m script. Then, run a demo script like one of these...

• testImageReconstruction.m: compressed-sensing recovery of a synthetic image using TV prior
• reconstructPendCar.m: compressed-sensing recovery of "PendCar" video frames
• testPreview.m: create preview images from synthetic datasets using a direct method with no optimization
• reconstructDMDVideosFromDatasets.m: recovery of videos from real emprical DMD measurements

Some notes

The stone transform is implemented as a simple linear operator that acts on vectors with power-of-four length. The transform itself is implemented in the compileable mex file STO_fast.c, and will need to be compiled before use. This compilation should hopefully happen automatically with you call setupSTO.m.

To apply the transform to an image, you need to map the image into a vector. First, call the createOrderingData.m method like so...
>> order = createOrderingData(256,'semi')
or
>> order = createOrderingData(256,'full')
This will create a struct called order that contrains information about the order in which image pixels should get mapped into a vector, assuming a 256x256 image size. The 'semi' options creates a more regular emebedding patters that produces smoother previews, while the 'full' option creates a highly random embedding that is a little better for compessed sensing, but creates more noisy previews.

Once you have the order struct, you can use it to map images into vectors. A stone transform on an image would look like this...

>> image = phantom(256);                      % Create 256x256 synthetic image . 
>> order = createOrderingData(256,'full');    % Create a struct with information on how to map image into vector  
>> vec = imageToNestedVector(image, order);   % Map the image into a vector using the specified pixel ordering    
>> transformed = STO(vec);                    % Apply the stone transform to the vector

To reverse this transform, one simply does this...

>> untransformed = STO(transformed);          % The stone transform is self-adjoint, so it's its own inverse
>> image = nestedVectorToImage(untransformed, order); % Map the 1D vector of pixels back into a 2D image array

Note this works because the stone transform is unitary. Therefore, the inverse stone transform is the same as the foreward stone tranform.