Multidimensional, high-resolution ultrasonic imaging of rapidly moving tissue is primarily limited by sparse sampling in the lateral dimension. In order to achieve acceptable spatial resolution and velocity quantization, interpolation of laterally sampled data is necessary. The authors present a novel method for estimating lateral subsample speckle motion and compare it with traditional interpolation methods. This method, called grid slopes, requires no a priori knowledge and can be applied to data with as few as two samples in the lateral dimension. Computer simulations were performed to compare grid slopes with two conventional interpolation schemes, parabolic fit and cubic spline. Results of computer simulations show that parabolic fit and cubic spline performed poorly at translations greater than 0.5 samples, and translations less than 0.5 samples were subject to an estimation bias. Grid slopes accurately estimated translations between 0 and 1 samples without estimation bias at high signal-to-noise ratios. Given that the grid slopes interpolation technique performs well at high signal-to-noise ratios, one pertinent clinical application might be tissue motion tracking