The paradigmatic example of signals with finite rate of innovation (FRI) is a linear combination of a finite number of Diracs per time unit, a.k.a. spike sequence. Many researchers have investigated the problem of estimating the innovative part of a spike sequence, i.e., time instants tks and weights cks of Diracs and proposed various deterministic or stochastic algorithms, particularly while the samples were corrupted by digital noise. In the presence of noise, maximum likelihood estimation method proved to be a powerful tool for reconstructing FRI signals, which is inherently an optimization problem. Wein and Srinivasan presented an algorithm, namely IterML, for reconstruction of streams of Diracs in noisy situations, which achieved promising reconstruction error and runtime. However, IterML is prone to limited resolution of search grid for tk, so as to avoid a phenomenon known as the curse of dimensionality, that makes it an inappropriate algorithm for applications that require highly accurate reconstruction of time instants. In order to overcome this shortcoming, we introduce a novel modified local best particle swarm optimization (MLBPSO) algorithm aimed at maximizing likelihood estimation of innovative parameters of a sparse spike sequence given noisy low-pass filtered samples. We demonstrate via extensive simulations that MLBPSO algorithm outperforms the IterML in terms of robustness to noise and accuracy of estimated parameters while maintaining comparable computational cost.

中文翻译：

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在嘈杂场景中重建有限创新信号率：一种稳健、准确的估计算法

具有有限创新率 (FRI) 的信号的典型示例是每时间单位有限数量的 Dirac 的线性组合，也就是尖峰序列。许多研究人员研究了估计尖峰序列的创新部分的问题，即 Diracs 的时刻 tks 和权重 cks，并提出了各种确定性或随机算法，特别是在样本被数字噪声破坏时。在存在噪声的情况下，最大似然估计方法被证明是重构 FRI 信号的有力工具，这本质上是一个优化问题。Wein 和 Srinivasan 提出了一种算法，即 IterML，用于在嘈杂情况下重建 Diracs 流，该算法实现了有希望的重建误差和运行时间。然而，IterML 容易受到 tk 搜索网格分辨率的限制，以避免出现称为维数灾难的现象，这使得它对于需要高度准确地重建时刻的应用程序来说是不合适的算法。为了克服这个缺点，我们引入了一种新颖的改进的局部最佳粒子群优化 (MLBPSO) 算法，旨在在给定噪声低通滤波样本的情况下最大化稀疏尖峰序列的创新参数的似然估计。我们通过广泛的模拟证明 MLBPSO 算法在噪声鲁棒性和估计参数的准确性方面优于 IterML，同时保持可比的计算成本。为了克服这个缺点，我们引入了一种新颖的改进的局部最佳粒子群优化 (MLBPSO) 算法，旨在在给定噪声低通滤波样本的情况下最大化稀疏尖峰序列的创新参数的似然估计。我们通过广泛的模拟证明 MLBPSO 算法在噪声鲁棒性和估计参数的准确性方面优于 IterML，同时保持可比的计算成本。为了克服这个缺点，我们引入了一种新颖的改进的局部最佳粒子群优化 (MLBPSO) 算法，旨在在给定噪声低通滤波样本的情况下最大化稀疏尖峰序列的创新参数的似然估计。我们通过广泛的模拟证明 MLBPSO 算法在噪声鲁棒性和估计参数的准确性方面优于 IterML，同时保持可比的计算成本。