Section: New Results
Emerging activities on Nonlinear Inverse Problems
Compressive sensing, compressive learning, audio inpainting, phase estimation
Locally-Linear Inverse Regression
Participant : Antoine Deleforge.
Main collaborations: Florence Forbes (MISTIS Inria project-team, Grenoble), Emeline Perthame (HUB team, Institut Pasteur, Paris), Vincent Drouard, Radu Horaud, Sileye Ba and Georgios Evangelidis (PERCEPTION Inria project-team, Grenoble)
A general problem in machine learning and statistics is that of high- to low-dimensional mapping. In other words, given two spaces
Audio Inpainting and Denoising
Participants : Rémi Gribonval, Nancy Bertin, Clément Gaultier.
Main collaborations: Srdan Kitic (Orange, Rennes)
Inpainting is a particular kind of inverse problems that has been extensively addressed in the recent years in the field of image processing. Building upon our previous pioneering contributions [54]), we proposed over the last three years a series of algorithms leveraging the competitive cosparse approach, which offers a very appealing trade-off between reconstruction performance and computational time [100], [102] [6]. The work on cosparse audio declipping which was awarded the Conexant best paper award at the LVA/ICA 2015 conference [102] resulted in a software release in 2016. In 2017, this work was extended towards advanced (co)sparse decompositions, including several forms of structured sparsityand towards their application to the denoising task.In particular, we investigated the incorporation of the so-called “social” structure constraint [103] into problems regularized by a cosparse prior [84], [85], and exhibited a common framework allowing to tackle both denoising and declipping in a unified fashion [82].
In 2018, a new algorithm for joint declipping of multichannel audio was derived and published [29]. Extensive experimental benchmarks were conducted, questioning the previous state-of-the-art habits in degradation levels (usually moderate to inaudible) and evaluation (small datasets, SNR-based performance criteria) and setting up new standards for the task (large and diverse datasets, severe saturation, perceptual quality evaluation) as well as guidelines for the choice of the best variant (sparse or cosparse, with or without structural time-frequency constraints...) depending on the data and operational conditions. These new results will be included in an ongoing journal paper, to be submitted in 2019.