In applications such as image processing, the data is given in a regular pattern with a known structure, such as a grid of pixels. However, it is becoming increasingly common for large datasets to have some irregular structure. In image recognition, one of the most successful methods is wavelet analysis, also commonly known as multi-resolution analysis. Our project is to develop and explore this powerful technique in the setting where the data is not stored in the form of a rectangular table with rows and columns of pixels. While the data sets will still have a lot of structure to be exploited, we want to extend the wavelet analysis to the setting when the data structure resembles is more like a network than a rectangular table. Networks provide a flexible generalization of the rigid structure of rectangular tables.
Dennis, Michael and Au-Yeung, Enrico
"Signal Processing on Graphs Using Kron Reduction and Spline Interpolation,"
DePaul Discoveries: Vol. 6
, Article 7.
Available at: http://via.library.depaul.edu/depaul-disc/vol6/iss1/7