This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors proposed for the one-dimensional problems. This note extends the eigenmatrix approach to multidimensional problems, providing a rather unified treatment for general kernels and unstructured sampling grids in both real and complex settings. Numerical results are provided to demonstrate the performance of the proposed method.

中文翻译：

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通过特征矩阵进行多维非结构化稀疏恢复


本说明考虑了多维非结构化稀疏恢复问题。示例包括 Fourier inversion 和 sparse deconvolution。特征矩阵是一种数据驱动的结构，具有为一维问题提出的所需的近似特征值和特征向量。本文将特征矩阵方法扩展到多维问题，为实数和复数设置中的一般内核和非结构化采样网格提供了相当统一的处理。给出了所提方法的性能。