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critically_sampled_wavelet_filterbanks_on_graphs
Critically Sampled Wavelet Filterbanks on Graphs

Sunil Kumar, USC

Wednesday, Jan 25, EEB 248, 2:00pm

Abstract: Graphs provide a very flexible model for representing data in many domains such as networks, non-uniformly sampled signals, and point clouds etc. The data on these graphs can be visualized as a finite collection of samples termed as ``graph-signals''. In this talk, I will present a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and down-sampling can be extended to the graph domain. In particular, I will describe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filterbanks, which cancel aliasing and lead to perfect reconstruction. I will present necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction in these filterbanks. For arbitrary graphs, I will present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. The proposed two-channel filterbanks can then constructed on each bipartite subgraph leading to “multi-dimensional” separable wavelet filterbanks on graphs.

Bio: I am a PhD student in the Ming Hsieh department of electrical engineering at USC. I am working with Prof Antonio Ortega and my research interests involve wavelet transforms on graphs, image and video processing. I am selected as one of the five MHI scholars for the academic year 2011-2012 and I am also an Annenberg Fellow from 2007 cohort. I received a BTech degree in electrical engineering from Indian Institute of Technology (IIT) Delhi, and have worked in IBM India Research Lab prior to joining USC.

Host: Alex Dimakis, dimakis [at] usc.edu

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