Segmenting T2-hyperintense white matter lesions from longitudinal MR images is essential in understanding progression of multiple sclerosis. Most lesion segmentation techniques find lesions independently at each time point, even though there are different noise and image contrast variations at each point in the time series. In this paper, we present a patch based 4D lesion segmentation method that takes advantage of the temporal component of longitudinal data. For each subject with multiple time-points, 4D patches are constructed from the T1-w and FLAIR scans of all time-points. For every 4D patch from a subject, a few relevant matching 4D patches are found from a reference, such that their convex combination reconstructs the subject's 4D patch. Then corresponding manual segmentation patches of the reference are combined in a similar manner to generate a 4D membership of lesions of the subject patch. We compare our 4D patch-based segmentation with independent 3D voxel-based and patch-based lesion segmentation algorithms. Based on ground truth segmentations from 30 data sets, we show that the mean Dice coefficients between manual and automated segmentations improve after using the 4D approach compared to two state-of-the-art 3D segmentation algorithms.