%0 Journal Article
%T Convex Optimization approach to signals with fast varying instantaneous frequency
%+ Modelling brain structure, function and variability based on high-field MRI data (PARIETAL)
%+ Laboratoire des signaux et systèmes (L2S)
%+ Department of Mathematics [University of Toronto]
%A Kowalski, Matthieu
%A Meynard, Adrien
%A Wu, Hau-Tieng
%Z Hau-tieng Wu’s work is partially supported by Sloan Research Fellow FR-2015-65363. Matthieu Kowalski benefited from the support of the ”FMJH Program Gaspard Monge in optimization and operation research”, and from the support to this program from EDF.
%< avec comité de lecture
%@ 1063-5203
%J Applied and Computational Harmonic Analysis
%I Elsevier
%V 44
%N 1
%P 89 - 122
%8 2018-01-01
%D 2018
%Z 1503.07591
%R 10.1016/j.acha.2016.03.008
%K Time-frequency analysis
%K Convex optimization
%K FISTA
%K Instantaneous frequency
%K Chirp factor
%Z Computer Science [cs]/Signal and Image Processing
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, which involves few properties an "ideal time-frequency representation" should satisfy, for example, the signal reconstruction and concentrative time frequency representation. FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) is applied to achieve an efficient numerical approximation of the functional. We coin the algorithm as {\it Time-frequency bY COnvex OptimizatioN} (Tycoon). The numerical results confirm the potential of the Tycoon algorithm.
%G English
%2 https://hal.science/hal-01199615v2/document
%2 https://hal.science/hal-01199615v2/file/TycoonACHARev1%20%281%29.pdf
%L hal-01199615
%U https://hal.science/hal-01199615
%~ CEA
%~ CNRS
%~ INRIA
%~ UNIV-PSUD
%~ INRIA-SACLAY
%~ SUP_LSS
%~ INRIA_TEST
%~ SUP_SIGNAUX
%~ TESTALAIN1
%~ CENTRALESUPELEC
%~ INRIA2
%~ CEA-UPSAY
%~ TDS-MACS
%~ UNIV-PARIS-SACLAY
%~ UNIV-PSUD-SACLAY
%~ CEA-UPSAY-SACLAY
%~ INRIA-SACLAY-2015
%~ CENTRALESUPELEC-SACLAY
%~ JOLIOT
%~ CEA-DRF
%~ NEUROSPIN
%~ INRIA2016-PREPRINT
%~ TEST-HALCNRS
%~ GS-ENGINEERING
%~ GS-COMPUTER-SCIENCE
%~ INRIAARTDOI
%~ INRIA-CANADA