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This paper approaches scatterometer image reconstruction as the inversion of a discrete noisy aperture-filtered sampling operation. Aperture-filtered sampling is presented and contrasted with conventional and irregular sampling. Discrete reconstruction from noise-free aperture-filtered samples is investigated and contrasted with conventional continuous reconstruction approaches. The discrete approach enables analytical treatment of the reconstruction grid resolution and the effective resolution imposed by the sampling and reconstruction operations. The noisy case is also explored. A reconstruction estimator based on maximum a posteriori (MAP) estimation is proposed to recover the conventional samples from noisy scatterometer measurements. This approach enables the scatterometer noise distribution to be appropriately accounted for in the reconstruction operation. The MAP and conventional reconstruction approaches are applied to the SeaWinds scatterometer and the Advanced Wind Scatterometer, and the effective resolution of the different methods is analyzed. The MAP approach produces results consistent with the well-established scatterometer image reconstruction (SIR) algorithm. The MAP approach significantly enhances the resolution at the expense of increased noise. Although a detailed noise-versus-resolution tradeoff analysis is beyond the scope of this paper, the new framework allows for a more general treatment than the ad hoc tuning parameters of the SIR algorithm.