  The problem of multivariate exponential analysis or sparse interpolation has
received a lot of attention, especially with respect to the number of samples
required to solve it unambiguously. In this paper we show how to bring the
number of samples down to the absolute minimum of $(d+1)n$ where $d$ is the
dimension of the problem and $n$ is the number of exponential terms. To this
end we present a fundamentally different approach for the multivariate problem
statement. We combine a one-dimensional exponential analysis method such as
ESPRIT, MUSIC, the matrix pencil or any Prony-like method, with some linear
systems of equations because the multivariate exponents are inner products and
thus linear expressions in the parameters.
