This talk will cover the material introduced by the three authors in their paper "Robust Uncertainty Principles", and by Candes and Romberg in "Sparsity and Incoherence in Compressive Sensing".

The basic question being answered is, how can one reconstruct a signal from incomplete (undersampled) measurements? These papers show that, if the signal is very sparse, there are techniques that will allow you to recover the signal exactly from a very small number of observations.