Analysis vs Synthesis-An Investigation of (Co) sparse Signal Models on Graphs

Madeleine Kotzagiannidis, Michael Davies

Research output: Contribution to conferencePaperpeer-review

Abstract / Description of output

In this work, we present a theoretical study of signals with sparse representations in the vertex domain of a graph, which is primarily motivated by the discrepancy arising from respectively adopting a synthesis and analysis view of the graph Laplacian matrix. Sparsity on graphs and, in particular, the characterization of the subspaces of signals which are sparse with respect to the connectivity of the graph, as induced by analysis with a suitable graph operator, remains in general an opaque concept which we aim to elucidate. By leveraging the theory of cosparsity, we present a novel (co)sparse graph Laplacian-based signal model and characterize the underlying (structured) (co)sparsity, smoothness and localization of its solution subspaces on undirected graphs, while providing more refined statements for special cases such as circulant graphs. Ultimately, we substantiate fundamental discrepancies between the cosparse analysis and sparse synthesis models in this structured setting, by demonstrating that the former constitutes a special, constrained instance of the latter.
Original languageEnglish
Publication statusAccepted/In press - 10 Sept 2018
EventIEEE Global Conference on Signal and Information Processing 2018 - Anaheim, United States
Duration: 26 Nov 201829 Nov 2018

Conference

ConferenceIEEE Global Conference on Signal and Information Processing 2018
Abbreviated titleGlobalSIP
Country/TerritoryUnited States
CityAnaheim
Period26/11/1829/11/18

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