不规则噪声样本的多维信号重构
Reconstruction of Multidimensional Signals from Irregular Noisy Samples
摘要：
我们专注于一个多维领域与不相关的频谱，并研究重建信号的质量时，现场样本是不规则的间隔和独立同分布的噪声的影响。更具体地说，我们应用线性重建技术，并采取的字段估计的均方误差（MSE）作为一个度量来评估信号重建质量。我们发现，MSE分析可以通过使用表示采样系统的矩阵的特征值分布的封闭形式的表达式进行。不幸的是，这种分布仍然是未知的。因此，我们首先推导出一个封闭形式的分布矩的表达式，我们发现，本征值分布趋于Marcenko-Pastur分布的场维数趋于无穷大。最后，通过使用我们的方法，我们得到了一个紧密的近似的MSE的重建领域。
英文摘要：
We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More specifically, we apply linear reconstruction techniques and take the mean square error (MSE) of the field estimate as a metric to evaluate the signal reconstruction quality. We find that the MSE analysis could be carried out by using the closed-form expression of the eigenvalue distribution of the matrix representing the sampling system. Unfortunately, such distribution is still unknown. Thus, we first derive a closed-form expression of the distribution moments, and we find that the eigenvalue distribution tends to the Marcenko-Pastur distribution as the field dimension goes to infinity. Finally, by using our approach, we derive a tight approximation to the MSE of the reconstructed field.
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