[en] Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode Decomposition technique and the Iterative Filtering method. When a signal contains mono-components that have rapid varying instantaneous frequencies like chirps or whistles, it becomes particularly hard for most techniques to properly factor out these components. The Adaptive Local Iterative Filtering technique has recently gained interest in many applied fields of research for being able to deal with non-stationary signals presenting amplitude and frequency modulation. In this work, we address the open question of how to guarantee a priori convergence of this technique, and propose two new algorithms. The first method, called Stable Adaptive Local Iterative Filtering, is a stabilized version of the Adaptive Local Iterative Filtering that we prove to be always convergent. The stability, however, comes at the cost of higher complexity in the calculations. The second technique, called Resampled Iterative Filtering, is a new generalization of the Iterative Filtering method. We prove that Resampled Iterative Filtering is guaranteed to converge a priori for any kind of signal. Furthermore, we show that in the discrete setting its calculations can be drastically accelerated by leveraging on the mathematical properties of the matrices involved. Finally, we present some artificial and real-life examples to show the power and performance of the proposed methods.Kindly check and confirm that the Article note is correctly identified.
Disciplines :
Mathematics
Author, co-author :
Barbarino, Giovanni ; Université de Mons - UMONS > Recherche > Service ERC Unit - Matrix Theory and Optimization
Cicone, Antonio; Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Coppito, Italy ; INAF, Istituto di Astrofisica e Planetologia Spaziali, Rome, Italy ; Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy
Language :
English
Title :
Stabilization and variations to the adaptive local iterative filtering algorithm: the fast resampled iterative filtering method
Publication date :
April 2024
Journal title :
Numerische Mathematik
ISSN :
0029-599X
eISSN :
0945-3245
Publisher :
Springer Science and Business Media Deutschland GmbH
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R450 - Institut NUMEDIART pour les Technologies des Arts Numériques
European Projects :
HE - 101085607 - eLinoR - Beyond Low-Rank Factorizations
AC thanks the Italian Ministry of the University and Research for the financial support under the PRIN PNRR 2022 grant number E53D23018040001 ERC field PE1 project P2022XME5P titled \u201CCircular Economy from the Mathematics for Signal Processing prospective\u201D, and the Ministry of Foreign Affairs and the International Cooperation for the financial support under the \u201CGrande Rilevanza\u201D Italy\u2014China Science and Technology Cooperation Joint Project titled \u201CsCHans\u2014Solar loading infrared thermography and deep learning teCHniques for the noninvAsive iNSpection of precious artifacts\u201D. GB is supported by the Alfred Kordelinin s\u00E4\u00E4ti\u00F6 grant no. 210122 and partly by an Academy of Finland grant (Suomen Akatemian P\u00E4\u00E4t\u00F6s 331240). GB is also supported by the European Union (ERC consolidator grant, eLinoR, no 101085607).The authors are members of the Italian \u201CGruppo Nazionale di Calcolo Scientifico\u201D (GNCS) of the Istituto Nazionale di Alta Matematica \u201CFrancesco Severi\u201D (INdAM).
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