Enhanced Cohen class time–frequency methods based on a structure tensor analysis: Applications to ISAR processing

Abstract

When dealing with time–frequency analysis, each distribution belonging to the Cohen class (CC) is defined by its kernel. It introduces a time–frequency smoothing which impacts on the time–frequency resolution and the cross-term disappearance. Depending on the application, the practitioner has to find the “best” compromise. In this paper, we suggest combining several CC time–frequency representations (TFRs), corresponding to coarse-to-fine scales of smoothing. Taking advantage of this diversity, our approach consists in differentiating the signal, assumed to be characterized by 2-D near-linear stable trajectories in the time–frequency plane, and the cross-terms, assumed to be geometrically unstructured. For this purpose, a “confidence map” for each TFR is deduced from a local variational analysis of the time–frequency distribution. The set of confidence maps is then used to combine the different TFRs in order to obtain an “enhanced” TFR. Our approach is compared with various conventional TFRs by using synthetic data. Despite a comparatively higher computational cost, the resulting enhanced TFR exhibits a high time–frequency resolution while having limited cross-terms. As simulation results confirm the effectiveness of our method, it is then applied in the field of inverse synthetic aperture radar (ISAR) processing.