Convex Optimization approach to signals with fast varying instantaneous frequency

Matthieu Kowalski (1, 2) , Adrien Meynard (2) , Hau-Tieng Wu (3)

1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
2 L2S - Laboratoire des signaux et systèmes
3 Department of Mathematics [University of Toronto]

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.

Mots clés: Time-frequency analysis; Convex optimization; FISTA; Instantaneous frequency; Chirp factor

Domaines: Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]

Matthieu Kowalski, Adrien Meynard, Hau-Tieng Wu. Convex Optimization approach to signals with fast varying instantaneous frequency. Applied and Computational Harmonic Analysis, 2018, 44 (1), pp.89 - 122. ⟨10.1016/j.acha.2016.03.008⟩. ⟨hal-01199615v2⟩