Name
Abstract | ||
|---|---|---|
In this work, we present extensions of the framework of sampling and reconstructing signals with a finite rate of innovation (FRI) to the graph domain, by tackling the problem of _R"-sparse graph signal reconstruction on perturbed circulant graphs, simulating network clusters within a large network. Given a dimensionality-reduced approximation of the GFT of the original graph signal, we develop a reconstruction approach, whereby, we operate on each subgraph individually using a set of approximation and denoising schemes. In particular, we employ a variation of Prony's method with Cadzow's algorithm, and further iterative denoising, which can lead to perfect reconstruction. In addition, we extend the application of recently developed circulant graph-wavelet fllterbanks to images featuring patterns, in a novel model inspired by image segmentation, which involves a localized operation of the graph wavelet transform on individual segments of homogeneous intensity content, employing the nearest circulant matrix approximation scheme. The proposed method outperforms traditional methods in the classical domain in nonlinear approximation performance. We give preliminary results and discuss generalizations to arbitrary graphs. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/GlobalSIP.2014.7032255 | Signal and Information Processing |
Keywords | Field | DocType |
approximation theory,channel bank filters,graph theory,image denoising,image reconstruction,image sampling,image segmentation,iterative methods,wavelet transforms,Cadzows algorithm,FRI,GFT,K-sparse graph signal reconstruction,Pronys method,circulant graph-wavelet filterbanks,dimensionality-reduced approximation,finite rate of innovation,graph wavelet transform,homogeneous intensity content,image processing,image segmentation,iterative denoising,nearest circulant matrix approximation scheme,network clusters,nonlinear approximation performance,perturbed circulant graphs,signal sampling,circulant graph,finite rate of innovation,graph wavelet filter-bank,image approximation | Iterative reconstruction,Adjacency matrix,Discrete mathematics,Algorithm,Image segmentation,Circulant matrix,Graph bandwidth,Sparse matrix,Mathematics,Signal reconstruction,Dense graph | Conference |
Citations | PageRank | References |
5 | 0.46 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Madeleine S. Kotzagiannidis | 1 | 12 | 1.92 |
| Dragotti, P.L. | 2 | 512 | 39.29 |