The spectrogram and its cousin, the scalogram, are at the basis of most audio processing algorithms: this signal representation seems to both preserve all the “perceptual” information contained in the signals, which is necessary to analyse them, and discard some “unnecessary” information, which could only confuse the algorithms. To give a theoretical content to this assertion, we will consider the problem of recovering a signal from its scalogram. We will explain that, at least for a specific choice of wavelets, all signals are (almost) uniquely determined by their scalogram, and that the reconstruction satisfies a form of local stability property. And since, for some applications, it would be desirable to have an implementable and efficient reconstruction algorithm, we will devote the last part of the talk to a discussion on possible algorithmic approaches.

Bio: I have defended a Phd in 2015, on phase retrieval for the scalogram and its applications to the scattering transform. After a one-year post-doctoral fellowship at MIT, I was recruited by CNRS. I am now a CNRS researcher at Université Paris Dauphine, and member of the Inria project-team Mokaplan, working on inverse problems and non-convex optimization.