Optical coherence tomography (OCT) has become an important modality for examination of the eye. To measure layer thicknesses in the retina, automated segmentation algorithms are often used, producing accurate and reliable measurements. However, subtle changes over time are difficult to detect since the magnitude of the change can be very small. Thus, tracking disease progression over short periods of time is difficult. Additionally, unstable eye position and motion alter the consistency of these measurements, even in healthy eyes. Thus, both registration and motion correction are important for processing longitudinal data of a specific patient. In this work, we propose a method to jointly do registration and motion correction. Given two scans of the same patient, we initially extract blood vessel points from a fundus projection image generated on the OCT data and estimate point correspondences. Due to saccadic eye movements during the scan, motion is often very abrupt, producing a sparse set of large displacements between successive B-scan images. Thus, we use lasso regression to estimate the movement of each image. By iterating between this regression and a rigid point-based registration, we are able to simultaneously align and correct the data. With longitudinal data from 39 healthy control subjects, our method improves the registration accuracy by 43% compared to simple alignment to the fovea and 8% when using point-based registration only. We also show improved consistency of repeated total retina thickness measurements.