Multiscale methods for data on graphs and irregular multidimensional situations

By Maarten Jansen, Guy P. Nason, Bernard Walter Silverman. 2009

95 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/423628f0ad62ab59252465ea6a4df2277aaa6b09

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

In Environmental Engineering

Citations in the corpus

Generalized Tree-Based Wavelet Transform (2010, methodology): “[10] proposed three methods whi ch were based on a variation of the lifting scheme [11], [12].”
A Multiscale Pyramid Transform for Graph Signals (2013, background): “Part of this work appeared in the master’s thesis [1] and was presented at the Duke Workshop on Sensing and Analysis of HighDimensional Data in July 2011.”
Multiscale Wavelets on Trees, Graphs and High Dimensional Data: Theory and Applications to Semi Supervised Learning (2010, background): “Jansen et al. (2009) explicitly state the lack of supporting theory for their methods: " The main disadvantage is that, apart from analogies with regular wavelets, there is currently no substantial body of theory behind our methods " .”
Wavelets on Graphs via Spectral Graph Theory (2009, unknown): “[32] develop a multiscale scheme for data on graphs based on lifting.”
Unbalanced Haar Technique for Nonparametric Function Estimation (2007, background): “We end this section by noting that the difference between the foregoing bottom-up algorithm and the “lifting one coefficient at a time” paradigm of Jansen, Nason, and Silverman (2006) is that in the latter work, the order of the detail coefficients to be computed depends only on the (irregular)…”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, background): “…the “top-down” wavelet construction of [54], graph dependent basis functions for sensor network graphs [55], lifting based wavelets on graphs [49], [56], multiscale wavelets on balanced trees [57], spectral graph wavelets [41], critically-sampled two-channel wavelet ﬁlter banks [37], [58], and a…”
Image denoising with nonlocal spectral graph wavelets (2010, methodology): “These include vertex-domain methods based on n-hop distance [14], lifting schemes [15], and methods restricted to trees [16].”