Generalized sampling and infinitedimensional compressed sensing
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will discuss a generalization of the Shannon Sampling Theorem
that allows for reconstruction of signals in arbitrary bases. Not only can one reconstruct in arbitrary bases, but this can also be done in a
completely stable way. When extra information is available, such as
sparsity or compressibility of the signal in a particular bases, one may reduce the number of samples dramatically. This is done via Compressed Sensing techniques, however, the usual finitedimensional framework is not sufficient. To overcome this obstacle I’ll introduce the concept of InfiniteDimensional Compressed Sensing.
This talk is part of the LMS Invited Lectures 2011 series.
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