Image reconstruction from discrete samples is fundamental in remote sensing. The reconstruction problem is more complicated when the sample locations are irregularly spaced and employ different aperture functions. Further, not all 2-D sampling configurations permit full image reconstruction of band-limited signals. In this article, 2-D signal reconstruction from irregular samples with variable apertures is considered using theory and examples. Exact reconstruction requires that the signal be band-limited and the sampling matrix be invertable. The results are sensitive to the sample locations and noise in the measurements. Illustrative examples are provided using simulation and actual data from the L-band Soil Moisture Active Passive (SMAP) radiometer. The general approach can be employed with other sensors.

中文翻译：

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不规则样本的离散带限信号重构

从离散样本重建图像是遥感的基础。当样本位置不规则间隔并采用不同的孔径函数时，重建问题会更加复杂。此外，并非所有的2D采样配置都允许对频带受限信号进行完整的图像重建。在本文中，使用理论和示例考虑了从具有可变孔径的不规则样本中重建二维信号的方法。精确的重建要求信号受到频带限制，并且采样矩阵是可逆的。结果对样品位置和测量中的噪声敏感。使用模拟和来自L波段土壤水分主动无源（SMAP）辐射计的实际数据提供了说明性示例。通用方法可以与其他传感器一起使用。