Persistence homology tools in signal processing
(09/2011 - 08/2015)
Individual research grant of Chinese Scholarship Council
Motivated by recent developments in topological persistence for assessment of the importance of features in data sets, we study the ideas of persistence homology for one- and two-dimensional digital signals and its application in signal denoising. Recently, notions of persistence homology and persistence pairs were introduced in for measuring the topological complexity of point sets in 3-D. Persistence pairs and corresponding persistence diagrams are well suited to quantify the topological significance of data structures and to develop a formalism for topological simplification. These approaches are exploited for adaptive signal and image denoising.
|Relation between total variation and persistence distance and its application in signal processing|
Gerlind Plonka, Yi Zheng
Advances in Computational Mathematics 42(3), 651-674, 2016, preprint (2014) as download.
|Application of persistent homology in signal and image denoising|
Dissertation, 2015, published online on 29 July 2015, http://hdl.handle.net/11858/00-1735-0000-001C-7131-B.