Mechanical oscillations or vibrations on spacecraft, also called pointing jitter, cause geometric distortions and/or smear in high-resolution digital images acquired from orbit. Geometric distortion is especially a problem with pushbroom sensors, such as the High Resolution Imaging Science Experiment (HiRISE) instrument on-board the Mars Reconnaissance Orbiter (MRO). Geometric distortions occur at a range of frequencies that may not be obvious in the image products, but can cause problems with stereo image correlation in the production of digital elevation models, and in measuring surface changes in time series with orthorectified images. The HiRISE focal plane comprises a staggered array of fourteen charge-coupled devices (CCDs) with pixel instantaneous field of view (IFOV) of 1 microradian. The high spatial resolution of HiRISE makes it both sensitive to, and an excellent recorder of jitter. We present an algorithm using Fourier analysis to resolve the jitter function for a HiRISE image that is then used to update instrument pointing information to remove geometric distortions from the image. Implementation of the jitter analysis and image correction is performed on selected HiRISE images made available to the public. Results show marked reduction of geometric distortions. This work has applications to similar cameras operating now (such as the Lunar Reconnaissance Orbiter Camera Narrow Angle Camera (LROC NAC) on-board the Lunar Reconnaissance Orbiter) and to the design of future instruments (such as the Europa Imaging System, planned for the Europa Clipper mission).