Localized Fourier analysis for graph signal processing
نویسندگان
چکیده
We propose a new point of view in the study Fourier analysis on graphs, taking advantage localization domain. For signal f vertices weighted graph G with Laplacian matrix L, standard relies functions g(L)f for some filters g IL, smallest interval containing spectrum sp(L)⊂IL. show that carefully chosen partitions IL=⊔1≤k≤KIk (Ik⊂IL), there are many advantages understanding collection (g(LIk)f)1≤k≤K instead directly, where LI is projected PI(L)L. First, partition provides convenient modelling theoretical properties and allows results (e.g. noise level estimation, support approximation). extend spectral wavelets to localized domain, called LocLets, we well-known frames can be written terms LocLets. From practical perspective, highlight interest proposed through experiments significant improvements two different tasks large estimation denoising. Moreover, efficient strategies permit compute sequence same time complexity as computation g(L)f.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2022
ISSN: ['1096-603X', '1063-5203']
DOI: https://doi.org/10.1016/j.acha.2021.10.004