Diffusion equations for adaptive affine distributions

We propose an extension of the adaptive diffusion technique for time-frequency representations proposed by P. Goncalves and E. Payot (see Proc. IEEE Digital Sig. Process. Workshop, 1998). Instead of processing time-frequency representations and keeping the covariance with respect to time and frequency shifts untouched, our adaptive filtering technique processes time-scale representations of the affine class while preserving the covariance properties of such representations. In order to obtain representations with improved readability, we aim at removing cumbersome interference terms while not blurring the signal terms. We show that the association of a conductance function to our diffusion scheme can make significant improvement toward reaching this goal. Indeed, a conductance function provides a way to adapt locally the amount of smoothing to the representation. Note that the adaptivity of this affine technique is not based on any waveform dictionary, such as matching pursuit algorithms.