从噪声样本中估计具有有限新息率的信号：一种随机算法
Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm
摘要：
作为最近引入的新息率概念的一个例子，可以通过线性滤波后进行均匀采样来获取作为每单位时间有限数量的Dirac的线性组合的信号。然而，实际上，样本很少是无噪声的。本文介绍了一种新的随机算法，用于从噪声样本中重建具有有限新息率的信号。即使这个问题的变体已经接近之前，满意的解决方案仅适用于某些类别的采样内核，例如内核满足的Strang-Fix条件。在本文中，我们考虑无限支持高斯核，它不满足Strang-Fix条件。可以采用其他类别的内核。我们的算法是基于吉布斯抽样，一个马尔可夫链蒙特卡罗（MCMC）方法。大量的数值模拟表明，我们的算法的准确性和鲁棒性。
英文摘要：
As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality, samples are rarely noiseless. In this paper, we introduce a novel stochastic algorithm to reconstruct a signal with finite rate of innovation from its noisy samples. Even though variants of this problem has been approached previously, satisfactory solutions are only available for certain classes of sampling kernels, for example kernels which satisfy the Strang-Fix condition. In this paper, we consider the infinite-support Gaussian kernel, which does not satisfy the Strang-Fix condition. Other classes of kernels can be employed. Our algorithm is based on Gibbs sampling, a Markov chain Monte Carlo (MCMC) method. Extensive numerical simulations demonstrate the accuracy and robustness of our algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
