February Fourier Talks 2013

This talk describes recent results on frame design which are motivated by communication theory. Finite frames are a natural tool for the linear encoding of analog signals. The linear dependencies among the frame vectors incorporate redundancy in the frame coefficients representing the signal, which allows to test the integrity of the encoded data and to correct errors that occur in its transmission. This talk discusses optimal frame design for recovery from partial data loss. We focus on structured data loss, that is, when packets become inaccessible or when consecutive frame coefficients are lost in a burst error. Essential techniques for frame design in this context come from the literature on compressed sensing.