#
Reconstruction and subgaussian processes

### Shahar Mendelson

Australian National University and Technion

### Abstract

In the reconstruction problem one is given a set T \subset \R^d and an unknown t \in T. The goal is to approximate this unknown point using
few random linear measurements (< X_i,t >)_{i=1}^k, where (X_i) are
selected independently according to a measure \mu on R^d. The question
is how to obtain high probability estimates on the degree of
approximation possible (depending on the number of measurements k,
properties of the set T and the measure \mu).

We will present a survey of recent results concerning the
reconstruction problem and explain how it could be analyzed using
properties of subgaussian processes.