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.