Robust and tractable multidimensional exponential analysis

Motivated by a number of applications in signal processing, we study the following question. Given samples of a multidimensional signal of the form {align*} f()=∑ₖ₌₁^K a_kexp(-i , _k), \\ _1,⋯,_k^q, \ ∈ ^q, \ || <n, {align*} determine the values of the number K of components, and the parameters aₖ and ₖ's. We develop an algorithm to recuperate these quantities accurately using only a subsample of size (qn) of this data. For this purpose, we use a novel localized kernel method to identify the parameters, including the number K of signals. Our method is easy to implement, and is shown to be stable under a very low SNR range. We demonstrate the effectiveness of our resulting algorithm using 2 and 3 dimensional examples from the literature, and show substantial improvements over state-of-the-art techniques including Prony based, MUSIC and ESPRIT approaches.