  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.
