Signal and image analysis algorithms play an important role in a variety of applications in science and technology. Examples include detecting cancer from image data, recognizing faces, reconstructing images from limited data (MRIs, CAT scans, etc.), and numerous others. Here you will find described new signal analysis and synthesis algorithms (i.e. transforms) derived based on comparing images (signals) using on not only their intensities, but also their respective locations. The goal of this project is to develop a framework for signal and image analysis that utilizes a 'Lagrangian' point of view. The approach relies heavily on optimal transport and related mathematical techniques. The study includes the development of invertible nonlinear signal transforms, efficient algorithms for their computation, and testing their application in a number of signal modeling and discrimination tasks (cancer detection, characterization of diseased cell phenotypes, visualization of variations in signal databases, recognition from low resolution images, and others). One main emphasis of the project is the development of Lagrangian transforms that have concrete theoretical and practical advantages in signal discrimination tasks.
Note: none of the programs or subprograms listed on this site are guaranteed in any way. They are relased under the Creative Commons GNU General Public License. To view a copy of this license, visit http://creativecommons.org/licenses/GPL/2.0. If you use any of the softwares above, please cite the accompanying article.
Funding provided by NSF award CCF 1421502