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EDP -asymptotic optimality. For cluster node x1, Kx 1 (left) scales like SRF 2ℓ 1 −2 , while the Ka 1 (right) scales like SRF 2ℓ 1 −1 . For the non-cluster node x4, both Kx 4 and Ka 4 are lower bounded by a constant. These scaling rates are optimal.

EDP -asymptotic optimality. For cluster node x1, Kx 1 (left) scales like SRF 2ℓ 1 −2 , while the Ka 1 (right) scales like SRF 2ℓ 1 −1 . For the non-cluster node x4, both Kx 4 and Ka 4 are lower bounded by a constant. These scaling rates are optimal.

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Fig. 1: (right) X has one cluster of size ℓ1 with SRF = 6. (left) X has...
Fig. 2: (right) single cluster configuration. (left) multi-cluster...
Fig. 3: EDP -asymptotic optimality. For cluster node x1, Kx 1 (left)...
Selecting Optimal Sampling Rate for Stable Super-Resolution
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  • Feb 2025
We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes ill-conditioned. Admissible sampling rates, or decimation parameters, improve the conditioning of the SR problem, enabl...
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... Figure 3, we numerically show that EDP is optimal, meaning it achieves the min-max error bounds (Theorem 2.8 in [5]) in the multi-cluster geometry. We plot the node/amplitude error amplification factors (6) as a function of SRF. ...

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