Remote sensing of ice motion by tracking displacement of surface features is a valuable tool in glaciology. Efficient image feature-tracking programs, such as IMCORR, based on fast Fourier transform methods can produce misleading correlations if there are data gaps in either or both of the reference and search images. This is particularly problematic if the data gaps are regular in character, such as for Landsat7 images collected after the failure of the Scan Line Corrector (SLC-off images). We demonstrate that this situation can be alleviated by filling the data gaps with suitably chosen random data. We modified IMCORR to achieve this automatically (source code is included), but generic image-processing software could be used to modify inputs for other correlation packages. We test our method using images of Pine Island Ice Shelf, Antarctica, and document the acceleration of the velocity field for the floating extension of Pine Island Glacier over the decade 2001–11. We also combine our velocities with recent NASA Operation IceBridge ice thickness data from CReSIS to estimate the basal melt rates.