Eigenmatrix for unstructured sparse recovery
This addresses sparse recovery challenges in various applications, but appears incremental as it builds on existing methods with a new construction.
The paper tackles unstructured sparse recovery problems, such as rational approximation and Fourier inversion, by proposing a data-driven eigenmatrix construction to handle noise and unstructured sample locations, demonstrating its efficiency through numerical results.
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are the noise in the sample values and the unstructured nature of the sample locations. This note proposes the eigenmatrix, a data-driven construction with desired approximate eigenvalues and eigenvectors. The eigenmatrix offers a new way for these sparse recovery problems. Numerical results are provided to demonstrate the efficiency of the proposed method.