Viernes 10 de Noviembre, 15:30 hs – Sala de Capacitación del Edif. de Administración del CCT.
Expositor: Rubén Spies
Título: “Adaptive multi-penalty regularization and a Bayesian approach to adaptivity in inverse problems: variable order smoothness priors”
Resumen In this seminar we will talk about adaptive regularization of inverse problems. Adaptivity (and in particular data-driven adaptivity) is relatively new in the area of inverse problems. Some results on multi-penalty heterogeneous and anisotropic regularization will be presented. In particular we will discuss ill-posed inverse problems from a statistical point of view with an emphasis on hierarchical variable order regularization. Traditionally, smoothness penalties in Tikhonov regularization assume a fixed degree of regularity of the unknown over the whole domain. Using a Bayesian framework with hierarchical priors, we derive a prior model, formally represented as a convex combination of autoregressive (AR) models, in which the parameter controlling the mixture of the AR models can dynamically change over the domain of the signal. Moreover, the mixture parameter itself is an unknown and is to be estimated using the data. Also, the variance of the innovation processes in the AR model is a free parameter, which leads to conditionally Gaussian priors that have been previously shown to be much more flexible than the traditional Gaussian priors, capable, e.g., to deal with sparsity type prior information. The suggested method, the Weighted Variable Order Autoregressive model (WVO-AR) is tested with a computed example. Some open problems will be discussed.
Bio: el Dr. Rubén D. Spies es Investigador Principal del CONICET, Profesor Titular de la UNL, Instituto de Matemática Aplicada del Litoral, IMAL, CONICET-UNL