Projects per year
Abstract
We consider the problem of characterizing the ‘duality gap’ between sparse synthesis- and cosparse analysis-driven signal models through the lens of spectral graph theory, in an effort to comprehend their precise equivalencies and discrepancies. By detecting and exploiting the inherent connectivity structure, and hence, distinct set of properties, of rank-deficient graph difference matrices such as the graph Laplacian, we are able to substantiate differences between the cosparse analysis and sparse synthesis models, according to which the former constitutes a constrained and translated instance of the latter. In view of a general union of subspaces model, we conduct a study of the associated subspaces and their composition, which further facilitates the refinement of specialized uniqueness and recovery guarantees, and discover an underlying structured sparsity model based on the graph incidence matrix. Furthermore, for circulant graphs, we provide an exact characterization of underlying subspaces by deriving closed-form expressions as well as demonstrating transitional properties between equivalence and non-equivalence for a parametric generalization of the graph Laplacian.
Original language | English |
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Pages (from-to) | 293-332 |
Journal | Applied and Computational Harmonic Analysis |
Volume | 60 |
Early online date | 16 Mar 2022 |
DOIs | |
Publication status | Published - 1 Sept 2022 |
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Dive into the research topics of 'Analysis vs synthesis with structure–An investigation of union of subspace models on graphs'. Together they form a unique fingerprint.Projects
- 2 Finished
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Next Generation Compressive and Computational Sensing and Signal Processing
Davies, M. (Principal Investigator)
1/10/16 → 30/09/21
Project: Research
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C-SENSE: Exploiting low dimensional models in sensing, computation and signal processing
Davies, M. (Principal Investigator)
1/09/16 → 31/08/22
Project: Research
Research output
- 1 Working paper
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Analysis vs Synthesis with Structure - An Investigation of Union of Subspace Models on Graphs
Kotzagiannidis, M. S. & Davies, M. E., 11 Nov 2018.Research output: Working paper