Hyperspectral cameras sample many different spectral bands at each pixel, enabling advanced detection and classification algorithms. However, their limited spatial resolution and the need to measure the camera motion to create hyperspectral images makes them unsuitable for nonsmooth moving platforms such as unmanned aerial vehicles (UAVs). We present a procedure to build hyperspectral images from line sensor data without camera motion information or extraneous sensors. Our approach relies on an accompanying conventional camera to exploit the homographies between images for mosaic construction. We provide experimental results from a low‐altitude UAV, achieving high‐resolution spectroscopy with our system.