"Sparse Frequency Estimation and the RIP"
Diederichs, BenediktSparse frequency estimation has attracted some attention in recent years. It is concerned with estimating the support of a sum of Dirac measures from a finite number of its Fourier coefficients. Similar to compressed sensing, the hope is to efficiently use the a priori information of sparsity, although sparsity in an infinite dimensional space is more difficult to exploit than in the finite dimensional case. In this talk, we introduce a stability result for frequency estimation similar to the restricted isometric property. Like in compressed sensing, we obtain a conditional well-posedness and a posteriori error estimates. To this end, we rely on extremal Fourier functions, which in turn can be motivated by classical results from sampling theory.