Name
Abstract | ||
|---|---|---|
We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary off the grid nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle), in the case when some of the nodes are separated by less than the inverse bandwidth. The bound is polynomial in the reciprocal of the so-called factor, while the exponent is controlled by the maximal number of nodes which are clustered together. This generalizes previously known results for the extreme cases when all of the nodes either form a single cluster, or are completely separated. We briefly discuss possible implications for the theory and practice of super-resolution under sparsity constraints. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Numerical Analysis | Discrete mathematics,Inverse,Singular value,Exponent,Polynomial,Matrix (mathematics),Mathematical analysis,Unit circle,Fourier transform,Vandermonde matrix,Mathematics |
DocType | Volume | Citations |
Journal | abs/1809.00658 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dmitry Batenkov | 1 | 25 | 7.19 |
| Laurent Demanet | 2 | 750 | 57.81 |
| Gil Goldman | 3 | 0 | 0.34 |
| yosef yomdin | 4 | 18 | 3.22 |