The miniaturization of hyperspectral cameras has opened a new path to capture spectral information. One such camera, called the hybrid linescan camera, requires accurate control of its movement. Contrary to classical linescan cameras, where one line is available for every band in one shot, the latter asks for multiple shots to fill a line with multiple bands. Unfortunately, the reconstruction is corrupted by a parallax effect, which affects each band differently. In this article, we propose a two-step procedure, which first reconstructs an approximate datacube in two different ways, and second, performs a corrective warping on each band based on a multiple homography framework. The second step combines different stitching methods to perform this reconstruction. A complete synthetic and experimental comparison is performed by using geometric indicators of reference points. It appears throughout the course of our experimentation that misalignment is significantly reduced but remains non-negligible at the potato leaf scale.