May 6-8-9, 2013

Facultad de Matemática y Computación, La Habana

Inverse Problems - Spectral Analysis - Time Series

This Spring-Summer School will consists in series of accessible lectures (6 hours in total for each speaker) on **inverse problems, spectral analysis and time series**.

- Yohann de Castro (Université Paris Sud)

**Compressed Sensing and Super-Resolution**

*We begin with the Compressed Sensing problem in high-dimensional regression. The main goal is to recover a (hign-dimensional) signal from few (random) linear measurements.*

In the second part of this course, we introduce the Super-resolution problem. We illustrate this problem as follows. In optical imaging, the physical limitations are evaluated by the resolution. This latter measures the minimal distance between lines that can be distinguished. Hence, the details below the resolution limit seem unreachable. The super-resolution phenomenon is the ability to recover the information beyond the physical limitations. Surprisingly, if the object of interest is simple (e.g. a discrete measure) then it is possible to override the resolution limit. In the mini-course, we will show how to extend the Compressed Sensing analysis to this framework. - Thibault Espinasse (Université Lyon 1)

**An introduction to random fields indexed by discrete structures**

*In this short lecture, we will consider a few classes of random fields indexed by discrete structures. Actually, the aim is to introduce different models of random fields indexed by graphs. We will first study Time series (that is, a random field indexed by Z), considering that Z is the simplest case. Then, we will give some extensions of Time series to the mutidimensional case (Z^d), following the book of X. Guyon. Finally, we will talk about graphical models, and try to understand the differences and the link between all theses objects.* - Paul Rochet (Université de Nantes)

**Variables selection issues in linear inverse problems**

*Heteroskedastic issues in general linear models can be apprehended as ill-posed inverse problems. The objective of this class is to give an overview of the modern regularization methods in inverse problems theory and their utility for treating specific issues such as model selection and aggregation of estimators.*

This school is addressed to non-specialists: participation of Graduate and PhD students is strongly encouraged.

There is no registration fee but registration is mandatory. Please fill the REGISTRATION FORM.

Schedule | M6 | W8 | T9 |
---|---|---|---|

09:30-11:30 | YdC | TE | PR |

13:00-15:00 | TE | PR | YdC |

15:00-17:00 | PR | YdC | TE |

Salomón Hernández, Luis Armando (salo 'at' matcom.uh.cu)