Stability of partial Fourier matrices with clustered nodes
Stability of partial Fourier matrices with clustered nodes
复制标题
具有簇节点的部分傅立叶矩阵的稳定性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Y. Yomdin
中科院分区：
文献类型：
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作者：
Dmitry Batenkov;L. Demanet;Gil Goldman;Y. Yomdin
我们证明，对于具有任意“ Off the Grid”节点的部分傅立叶矩阵的最小奇异值的急剧下限（等效地，在单位圆圈上具有节点的矩形vandermonde矩阵），如果某些节点被某些节点通过小于逆带宽。在所谓的“超分辨率因子”的倒数中，界限是多项式的，而指数由聚集在一起的最大节点数量控制。当所有节点都形成一个单个群集或完全分离时，这将在极端情况下概括为极端情况。我们简要地讨论了在稀疏限制下对超分辨率的理论和实践的可能影响。
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 "super-resolution 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.