Illustration of the stitching problem for two cubes. On the left, one can observe that the shortest wavelength cube in blue has a better spatial resolution (as illustrated by the finer grid) and a smaller field of view than the longest wavelength cube in red. The space-wavelength supports of the cubes partially overlap. The coarse stitching procedure shown in Fig. 1a sacrifices spatial resolution, while Haute Couture shown in Fig. 1b enables the reconstruction of a cube with the best spatial resolution over the full range of wavelengths.