Discrete Band-Limited Signal Reconstruction From Irregular Samples

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.