论文标题
来自非均匀样品的流媒体重建
Streaming Reconstruction from Non-uniform Samples
论文作者
论文摘要
我们提出了一种在线算法，用于从一组非均匀样品中重建信号。通过使用紧凑的基础函数表示信号，我们显示如何以流方式估算最小二乘的扩展系数：作为流程的方式：作为随后的时间间隔的样本批次，算法构成算法的初始估计值，然后在先前的间隔上更新信号间隔的初始估计。我们给出了该重建过程稳定的条件，并表明每个间隔中最小二乘的估计值呈指数收敛，这意味着可以使用有限的内存执行更新，而精度几乎没有损失。我们还讨论了我们的框架如何扩展到更一般的测量类型，包括与紧凑的核心内核相变的卷积。
We present an online algorithm for reconstructing a signal from a set of non-uniform samples. By representing the signal using compactly supported basis functions, we show how estimating the expansion coefficients using least-squares can be implemented in a streaming manner: as batches of samples over subsequent time intervals are presented, the algorithm forms an initial estimate of the signal over the sampling interval then updates its estimates over previous intervals. We give conditions under which this reconstruction procedure is stable and show that the least-squares estimates in each interval converge exponentially, meaning that the updates can be performed with finite memory with almost no loss in accuracy. We also discuss how our framework extends to more general types of measurements including time-varying convolution with a compactly supported kernel.
