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A Subvolume-based algorithm for elastic Ultrasound REgistration (SURE) was developed and evaluated. Designed primarily to improve spatial resolution in three-dimensional compound imaging, the algorithm registers individual image volumes nonlinearly before combination into compound volumes. SURE works in one or two stages, optionally using MIAMI Fuse© software first to determine a global affine registration before iteratively dividing the volume into subvolumes and computing local rigid registrations in the second stage. Connectivity of the entire volume is ensured by global interpolation using thin-plate splines after each iteration. The performance of SURE was quantified in 20 synthetically deformed in vivo ultrasound volumes, and in two phantom scans, one of which was distorted at acquisition by placing an aberrating layer in the sound path. The aberrating layer was designed to induce beam aberrations reported for the female breast. Synthetic deformations of 1.5-2.5 mm were reduced by over 85% when SURE was applied to register the distorted image volumes with the original ones. Registration times were below 5 min on a 500-MHz CPU for an average data set size of 13MB. In the aberrated phantom scans, SURE reduced the average deformation between the two volumes from 1.01 to 0.30mm. This was a statistically significant (P=0.01) improvement over rigid and affine registration transformations, which produced reductions to 0.59 and 0.50 mm, respectively.