In this talk, I will consider the group of signals which can be (precisely) reconstructed from a finite number of samples. More specifically, I talk about the class of signals with sparse representation in a known domain and signals with finite rate of innovations (FRI). The recently introduced framework of infinite-dimensional compressed seining shows that the signals in the former class can be recovered from a finite number of random samples in a different domain. The recovery algorithm solves a basis pursuit problem after a proper selection of the range and the number of random samples. On the other hand, in the latter class, a limited group of FRI signals can be reconstructed from carefully-chosen samples using the annihilating filter method. This method is very sensitive to noise and cannot be easily generalized to all of the signals in this class. Motivated by the infinite-dimensional compressed sensing, I am trying to find a new recovery algorithm for FRI signals by solving a basis pursuit problem. The new algorithm (if it succeeds) will be more robust to the noise and can be extended to all of the signals in this class.
April 9th, Mitra
Posted by Runwei Zhang on Thursday 23 January 2014 at 13:12