Selecting Optimal Sampling Rate for Stable Super-Resolution

TL;DR

This paper explores how choosing the right sampling rate can improve the stability and accuracy of super-resolution in spike train signals, especially when nodes are closely spaced, by proposing an efficient method to identify optimal sampling parameters.

Contribution

It introduces a novel preprocessing approach to determine the optimal sampling rate, enhancing super-resolution recovery performance in challenging conditions.

Findings

Optimal sampling rates improve SR stability.

Preprocessing method enhances recovery accuracy.

Method effective for closely spaced nodes.

Abstract

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, enabling more accurate recovery. We propose an efficient preprocessing method to identify the optimal sampling rate, significantly enhancing the performance of SR techniques.