Research Outline

I am currently working on sampling theory, more specifically within the framework of the recently developed theory of sampling signals with Finite Rate of Innovation (FRI). Certain parametric signals can be characterised by a finite number of parameters, which leads to far fewer degrees of freedom than the signal's Nyquist rate samples. This is the basis for the exact results that were originally derived in the context of FRI theory, first using the sinc kernel and later on extended to kernels of compact support.

When noise is present the ideal derivations are no longer valid and alternative techniques are needed. Empirical observations indicate that, for some noisy FRI signals, substantial performance improvements are achievable when the sampling rate is increased beyond the rate of innovation. One are of active r esearch on FRI is therefore the development of algorithms with improved noise robustness. The effect of digital noise on the recovery procedure has been previously analysed for the sinc case, and an optimal methodology based on subspace techniques has been proposed.

My goal is to improve the performance of sampling and recovering FRI signals when we use certain types of kernels of compact support that can reproduce exponentials. In addition, part of my research has been conducted to the application of FRI theory on Neuroscience. More specifically, we are trying to derive alternative to existing ways to measure various types of neuron activity in a compressed form.

My work was supported during 2 years by the non-profit organisation Fundación Caja Madrid. It is currently funded by my supervisor, Dr. Pier Luigi Dragotti.