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Robust and tractable multidimensional exponential analysis
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DOI：10.1007/s11075-025-02259-7.png)
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Abstract
En 中文
Motivated by a number of applications in signal processing, we study the following question. Given samples of a multidimensional signal of the form f(& ell;) = & sum;(K)(k=1) a(k) exp(-i <& ell;, w(k)>), w(1), , w(k) is an element of R-q, & ell; is an element of Z(q), |& ell;| < n, determine the values of the number K of components, and the parameters ak and wk's. We note that the the number of samples of f in the above equation is (2n - 1)(q). We develop an algorithm to recuperate these quantities accurately using only a subsample of size O(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.
Keywords:
Exponential sums
Localized kernels
Digital signal separation
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