Deconvolution with unknown noise distribution for structured signals

Vortrag von Dr. Luc Lehéricy

Sprecher eingeladen von: Prof. Dr. Delia Marina Coculescu

Datum: 14.11.24  Zeit: 12.15 - 13.45  Raum: Y27H12

Abstract. Deconvolution is the problem of recovering the distribution of a signal X based on noisy observations Y = X + epsilon. Most existing results require stringent assumptions on the noise distribution, for example that it is known, or that an auxiliary sample from the noise distribution is available. In this talk, I will show that it is possible to recover the distribution of the hidden signal with almost no assumption on the noise and no auxiliary sample, provided the signal is multidimensional with some dependency between its components. I also show how to use this result to construct estimators of the distribution of the signal and of its support, with rates of convergence that are minimax optimal. This talk is based on joint works with Elisabeth Gassiat, Sylvain Le Corff and Jérémie Capitao-Miniconi.