Anisotropic diffusion equations for adaptive quadratic representations

Adaptive diffusion techniques for processing time-frequency representations were first proposed by Payot and Gonçalvès in 1998 as an application of the Perona and Malik adaptive diffusion. In this communication we consider both this technique and the anisotropic diffusion of Weickert, which allows to tune orientation and shape of smoothing kernels. We propose a new adaptive diffusion scheme where the strength and the orientation of the anisotropic kernel are locally tailored to the processed time-frequency representation. We provide a comparison with other signal-dependent techniques. Finally we define a diffusion tensor that can be used to process time-frequency representations of the affine class, ensuring the preservation of their covariance properties.