Interpolation of ultrasound data at regular grid locations is provided by simultaneously optimizing interpolated data according to fidelity of interpolation of the voxel data to actual measured spatial data and according to a gradient of the interpolated data. This process is made amenable to real-time processing by limiting the range of interpolation to produce a sparse interpolated matrix that may be readily inverted. Artifacts and inefficiencies from successive stages of interpolation and data smoothing are thereby avoided.
