Sparsity Through Annihilation: Algorithms and Applications

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• Prof. Thierry Blu (CUHK)
• Tuesday 11 July 2023, 14:30-16:00
• Denis Gabor Seminar Room, 611.

If you have a question about this talk, please contact Ayush Bhandari.

Abstract The problem of reconstructing or estimating partially observed or sampled signals is an old and important one, and finds application in many areas that involve data acquisition. Traditional sampling and reconstruction approaches are heavily influenced by the classical Shannon sampling theory which gives an exact sampling and interpolation formula for bandlimited signals.

Within the last two decades, the classical Shannon sampling framework has been extended to classes of non-bandlimited structured signals, which we call signals with Finite Rate of Innovation. In these new sampling schemes, the prior that the signal is sparse in a basis or in a parametric space takes the form of a linear system of equations expressing the annihilation of signal-derived quantities. The coefficients of this annihilation system are then related in a non-linear way (e.g., polynomial roots) to the sparse signal parameters; i.e., its “innovations”. This leads to new exact reconstruction formulas and fast algorithms that achieve such reconstructions.

We will show how these algorithms are able to deal succesfully with noise issues, leading to statistically optimal recovery, and we will exemplify this theory with a number of applications that benefit from these novel schemes.

Speaker Bio Th. Blu was born in Orléans, France in 1964. He graduated (MSc) from École polytechnique (Paris, France) in 1986. Then, in 1988, he graduated (MEng) from École Nationale Supérieure des Télécommunications (Paris, France) from which he also obtained a PhD in electrical engineering (1996). From 1988 to 1998, he worked at France Telecom R&D (now “Orange”) as a research engineer first in Hertzian wave propagation, then in signal processing and videotelephony. He has been on leave from the French administration (1998 to 2014), with the rank of “Ingénieur en Chef des Mines”. In 1998, Th. Blu joined the Biomedical Imaging Laboratory, then recently created by Prof. Michael Unser at EPFL (Lausanne, Switzerland), where he became responsible for the mathematical aspects of image processing in connection with biomedical/biological data. Th. Blu left EPFL at the end of 2007 to join the Department of Electronic Engineering at the Chinese University of Hong Kong, where he is currently a tenured professor.

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