{"title":"谱图小波包帧","authors":"Iulia Martina Bulai , Sandra Saliani","doi":"10.1016/j.acha.2023.04.003","DOIUrl":null,"url":null,"abstract":"<div><p>Classical wavelet, wavelet packets<span> and time-frequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs.</span></p><p>We will give some concrete examples on how the spectral graph wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph with 900760 nodes, representing the brain voxels.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"66 ","pages":"Pages 18-45"},"PeriodicalIF":2.6000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spectral graph wavelet packets frames\",\"authors\":\"Iulia Martina Bulai , Sandra Saliani\",\"doi\":\"10.1016/j.acha.2023.04.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Classical wavelet, wavelet packets<span> and time-frequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs.</span></p><p>We will give some concrete examples on how the spectral graph wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph with 900760 nodes, representing the brain voxels.</p></div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"66 \",\"pages\":\"Pages 18-45\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1063520323000313\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520323000313","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Classical wavelet, wavelet packets and time-frequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs.
We will give some concrete examples on how the spectral graph wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph with 900760 nodes, representing the brain voxels.
期刊介绍：
Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.
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