Finding the right model for our data

CARLOS CABRELLI

Nashville

Conferencia; 5th International Conference on Computational Harmonic Analysis; 2014

Vanderbilt University

Finding the right model for given data Assume that we need to process a large amount of data that we know is low dimensional. ​A comm ​o​n practice ​in this case, is to impose some ​​hypothesis on the data and use a standard model. For example we can assume that the data is band limited, then we can use an appropriate Paley-Wiener space. A more realistic approach is to select a big class of models (subspaces) and try to find the one that best fit our data. In this talk we will show that this is possible in many situations. ​In particular we i ​l​lustrate this in the space L^2(\R^N), with shift invariant spaces, having extra-invariance, which provide a model for noisy data and give a way to control the jitter error.