We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used to estimate the pulse locations. However, existing theoretical analysis is restricted to ideal assumptions on signal and measurement models. We present a novel perturbation analysis that overcomes the previous theoretical limitation, which is derived without a stringent assumption on the signal model. Our unifying analysis applies to various sub-array designs of the ESPRIT algorithm. We demonstrate the usefulness of the perturbation analysis by specifying the result in two practical scenarios. In the first scenario, we quantify how the number of snapshots for stable recovery scales when the number of Fourier measurements per snapshot is sufficiently large. In the second scenario, we propose compressive blind array calibration by ESPRIT with random sub-arrays and provide the corresponding non-asymptotic error bound applying uniformly to all well-separated pulses. Furthermore, we demonstrate that the empirical performance of ESPRIT corroborates the theoretical analysis through extensive numerical results.

中文翻译：

---

通过 ESPRIT 从多个快照稳定估计未知形状的脉冲


我们考虑解决来自噪声多快照测量的重叠脉冲的问题，这一直是包括医学成像和阵列信号处理在内的各种应用的核心问题。 ESPRIT 算法已用于估计脉冲位置。然而，现有的理论分析仅限于信号和测量模型的理想假设。我们提出了一种新颖的扰动分析，克服了先前的理论限制，该分析是在没有对信号模型进行严格假设的情况下得出的。我们的统一分析适用于 ESPRIT 算法的各种子阵列设计。我们通过在两个实际场景中指定结果来证明扰动分析的有用性。在第一种情况下，我们量化当每个快照的傅里叶测量数量足够大时，稳定恢复的快照数量如何扩展。在第二种情况下，我们提出通过 ESPRIT 与随机子阵列进行压缩盲阵列校准，并提供相应的非渐近误差界，均匀地应用于所有分离良好的脉冲。此外，我们证明 ESPRIT 的实证性能通过大量数值结果证实了理论分析。