The Blahut/Ben-Or/Tiwari sparse interpolation algorithm from computer algebra is closely related to Prony’s method for exponential analysis. In this talk, we focus on some challenges in exponential analysis.

Estimating the spectral information of an exponential sum plays an important role in many signal processing applications. In particular, we mention the direction of arrival (DOA) problem in smart antenna technology and nuclear magnetic resonance (NMR) spectroscopy.

We present a parametric method to retrieve high-resolution information from coarse-scale measurements. In the multivariate case, our method can identify and separate distinct multivariate parameters from the minimal number of samples. If time permits, we will discuss the connection between multivariate exponential analysis and tensor decomposition, which may lead to new possibilities to exploit sparsity in analyzing tensor-structured datasets.