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This paper approaches wind field estimation from scatterometer measurements as the inversion of a noisy nonlinear sampling operation. The forward sampling model is presented and made discrete for practical purposes. Generally, the wind estimation problem is ill-posed at high resolution, which means that there are more parameters to estimate than measurements. A Bayesian approach based on maximum a posteriori (MAP) estimation is proposed to regularize the problem. This allows the simultaneous estimation of the regular samples of the high-resolution wind vector field directly from the noisy aperture-filtered backscatter σ° measurements. The MAP reconstruction approach is applied to the SeaWinds scatterometer, the examples are presented, and the results are compared to standard products. The MAP reconstruction method produces results that are consistent with standard products while preserving the higher spatial resolution information. The MAP estimates result in a similar resolution to the standard ultrahigh-resolution processing method but with a lower bias and a lower variability in the estimates.