Staggered time delay and integration (TDI) scanning image acquisition systems are usually employed in low signal-to-noise situations such as thermal imaging. Analysis and restoration of images acquired by thermal staggered TDI sensors in the presence of mechanical vibrations that may cause space-variant image distortions (severe geometric warps and blur) are studied. The relative motion at each location in the degraded image is identified from the image when a differential technique is used. This information is then used to reconstruct the image by a technique of projection onto convex sets. The main novelty is the implementation of such methods to scanned images (columnwise). Restorations are performed with simulated and real mechanically degraded thermal images.