Half-quadratic regularization of time-frequency AR analysis for recovery of abrupt spectral discontinuities & their detection by a recursive Siegel metric based on information geometry

We have proposed in [1][2] a Thikonov approach of Burg algorithm regularization based on a local quadratic potential function which yields a smoothness constraint with a long AR model. We propose to extend regularization approach in time-frequency domain with a temporal smoothness constraint. First, we use an half-quadratic regularization that avoids classical oversmoothing effect of quadratic potential function and preserves abrupt spectral changes and discontinuities. Secondly, to improve time-frequency dissimilarity detection, we propose a new recursive Siegel metric for AR models based on information differential geometry introduced by Rao through Fisher information matrix and Shannon entropy functional.