Adaptive diffusion as a versatile tool for time-frequency and time-scale representations processing: a review

Inspired by the work on image processing by Perona and Malik, diffusion-based models were first investigated by Goncalve`s and Payot to improve the readability of Cohen class time-frequency representations. They rely on signal-dependent partial differential equations that yield adaptive smoothed representations with sharpened time-frequency components. Here, we demonstrate the versatility and utility of this family of methods, and we propose new adaptive diffusion processes to locally control both the orientation and the strength of smoothing. Our approach is an improvement on previous works as it provides a unified framework not only for the Cohen class but for the affine class as well. The latter is of particular interest because, except for some special techniques such as the reassignment method, no signal-dependent smoothing technique exists to process bilinear time-scale distributions, nor even a transposition of the adaptive optimal-kernel method proposed by Baraniuk and Jones.