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Observed medical ultrasound images are degraded representations of the true acoustic tissue reflectance. The degradation is due to blur and speckle, and significantly reduces the diagnostic value of the images. In order to remove both blur and speckle we have developed a new statistical model for diffuse scattering in 2D ultrasound radio-frequency images, incorporating both spatial smoothness constraints and a physical model for diffuse scattering. The modeling approach is Bayesian in nature, and we use Markov chain Monte Carlo methods to obtain the restorations. The results from restorations of some real and simulated radio-frequency ultrasound images are presented and compared with results produced by Wiener filtering.