SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page B675-B695, January 2020.
We present a $d$-dimensional exponential analysis algorithm that offers a range of advantages compared to other methods. The technique does not suffer the curse of dimensionality and only needs $O((d+1)n)$ samples for the analysis of an $n$-sparse expression. It does not require a prior estimate of the sparsity $n$ of the $d$-variate exponential sum. The method can work with sub-Nyquist sampled data and offers a validation step, which is very useful in low SNR conditions. A favorable computation cost results from the fact that $d$ independent smaller systems are solved instead of one large system incorporating all measurements simultaneously. So the method easily lends itself to a parallel execution. Our motivation to develop the technique comes from 2-D and 3-D radar imaging and is therefore illustrated on such examples.

中文翻译：

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稀疏多维指数分析及其在雷达成像中的应用

SIAM科学计算杂志，第42卷，第3期，第B675-B695页，2020年1月。
我们提出了一种$ d $维指数分析算法，与其他方法相比，该算法具有一系列优势。该技术不会遭受维数的诅咒，只需要$ O（（d + 1）n）$个样本即可分析$ n $稀疏表达式。它不需要对$ d $变量指数总和的稀疏$ n $进行事先估计。该方法可以处理亚奈奎斯特采样数据，并提供验证步骤，这在低SNR条件下非常有用。有利的计算成本来自以下事实：解决了$ d $个独立的较小系统，而不是一个同时包含所有测量值的大型系统。因此，该方法很容易实现并行执行。我们开发该技术的动机来自2-D和3-D雷达成像，因此在此类示例中进行了说明。