Compressive Sampling

Start: 11/14/2007 - 3:15pm
End  : 11/14/2007 - 4:15pm


Prof. Emmanuel Candes, California Institute of Technology


One of the central tenets of signal processing is the Shannon-Nyquist sampling theory: the numbers of samples needed to reconstruct a signal without error is dictated by its bandwith, namely the shortest interval which contains the support of the spectrum of the signal under study. Veryrecently, an alternative sampling or sensing theory has emerged which goes against the conventional wisdom. This theory allows the faithfulrecovery of signals and images from what appear to be highly incomplete sets of data, i.e. from far fewer data that tradinal methods use. Underlying this methodology is a concrete protocol for sensing and compressing data simultaneously.
This talk will present the key mathematical ideas underlying this new sampling or sensing theory, and will survey some of the most important results. We will argue that this is a robust mathematical theory; not only it is possible to recover signals accurately from just an incomplete sets of measurements, but it is also possible to do so when the measurements are unrealiable and corrupted by noise.