Foundation Award for Research

Kanghui Guo

Kanghui Guo

Mathematics
College of Natural and Applied Sciences

I. Focus of Research

Professor D. Labate and I initiated the Shearlet system around 2004. The new system was first appeared in the paper "Optimally Sparse Multidimensional Representation using Shearlets" published in a prestigious journal for applied mathematics: SIAM J Math. Anal., 39 (2007), 298–318. Today the Shearlet system has been established as one of the most flexible and powerful multiscale methods for the analysis and processing of multidimensional functions and signals: the aforementioned paper was cited more than 250 times and almost 3000 documents on Shearlets were found on a recent Google Scholar search. The Shearlet approach combines the power of multiscale analysis with the ability to efficiently capture the directional and geometric information. Thanks to these properties, it enables sparse expansions of functions and operators, efficient extraction of the microlocal properties of distributions and this can be translated into efficient algorithms for inverse problems (Radon transform), image and signal processing (data restoration and enhancement) and pattern recognition (feature extraction and classification). Our research projects resulted in 20 peer-reviewed journal articles since 2007 and was funded by NSF (2010–2014).

II. Major Projects

  • Development  of  continuous and discrete Shearlets  (2003–2004)
  • Study multidimensional data with discrete Shearlets (2006–2012)
  • Study images and Radom transforms with continuous and discrete Shearlets (2009–present).

III. Future Directions of Research

As the theoretical development has been done, we will focus on the application of Shearlets to various problems in the real world. A special effort will be given to the medical imaging and large biological data.

IV. Topics related to your research and of interest to the broad University Community, for which you are available for presentations and/or consultations.

  • Mathematics and biology.
  • Detect an edge of an image with Shearlets
  • The new development of Fourier analysis