### iTWIST’16 Keynote Speakers: Lieven Vandenberghe

The workshop program has been ready for some time now, and we are handling the final practicalities to be ready to welcome you in Aalborg in August for the iTWIST’16 workshop. So now I think it is time to start introducing you to our – IMO – pretty impressive line-up of keynote speakers.

First up is Prof. Lieven Vandenberghe from UCLA. Prof. Vandenberghe is an expert on convex optimisation and signal processing and is – among other things – well known for his fundamental textbook “Convex Optimization” together with Steven Boyd.

Lieven Vandenberghe is Professor in the Electrical Engineering Department at UCLA. He joined UCLA in 1997, following postdoctoral appointments at K.U. Leuven and Stanford University, and has held visiting professor positions at K.U. Leuven and the Technical University of Denmark. In addition to “Convex Optimization”, he also edited the “Handbook of Semidefinite Programming” with Henry Wolkowicz and Romesh Saigal.

At iTWIST, I am looking forward to hearing him speak about Semidefinite programming methods for continuous sparse optimization. So far, it is my impression that most theory and literature about compressed sensing and sparse methods has relied on discrete dictionaries consisting of a basis or frame of individual dictionary atoms. If we take the discrete Fourier transform (DFT) as an example, the dictionary has fixed atoms corresponding to a set of discrete frequencies. More recently, theories have started emerging that allow continuous dictionaries instead (see for example also the work of Ben Adcock, Anders Hansen, Bogdan Roman et al. as well). As far as I understand – a generalisation that in principle allows you to get rid of the discretised atoms and consider any atoms on the continuum “in between” as well. This is what Prof. Vandenberghe has planned for us so far (and this is joint work with Hsiao-Han Chao):

We discuss extensions of semidefinite programming methods for 1-norm minimization over infinite dictionaries of complex exponentials, which have recently been proposed for superresolution and gridless compressed sensing.

We show that results related to the generalized Kalman-Yakubovich-Popov lemma in linear system theory provide simple constructive proofs for the semidefinite representations of the penalties used in these problems. The connection leads to extensions to more general dictionaries associated with linear state-space models and matrix pencils.

The results will be illustrated with applications in spectral estimation, array signal processing, and numerical analysis.