My research interests lie on the boundary of sampling theory and machine learning,
specifically in the design of adaptive samplers. Although this seems like a natural approach,
allowing nonuniform sample sets, extending the notion of a sample and using nonlinear
sampling devices introduces a number of difficulties in the analysis and recovery of such schemes.
The 4 main topics in my research focus on:
1) Reconstruction algorithms
2) Learning from unequally spaced time series
3) Efficient encoding of neural and ECG data
4) Establishing a framework for the design of samplers based on linear dynamical systems.
These problems are related to a wide range of topics:
1) Frame theory, Sampling from local averages, Splines
2) Point process distances, spike decoding, here we know the input signal and the transformation that generates these point processes.
3) Real time recovery algorithms, spike sorting
4) Kalman filtering, H_\infty control, Unknown input observer
Any sampling framework is composed of three basic elements. First we require a description of the signals of interest. We are interested in applications, specifically for BMI (neural data) and ECG. Next, the encoder must be designed, currently we are working on a framework for adaptive samplers assuming they can be modeled by a linear dynamical system, which is where we overlap with control theory concepts such as sampleddata systems and H\infty control. Finally, the samples can be used to recover the original signal or directly extract information from them.
This second approach implies that for timebased encoders (i.e. linear dynamical systems whose output is sampled using level crossings) such as the IF family, we are looking for operations on point process. In contrast to the more genearl framework usually treated in the computational neuroscience community, here we assume a known transformation on a specific input space which generates this process. Therefore we can include more information in the design of sample set distances. These can later be applied in a learning algorithm; for example, spike sorting for BMI applications and parameter selection based on sample metrics.
