We present a fast reconstruction algorithm for hyperspectral images, utilizing a small amount of data without the need for any training. The method is implemented with a dual disperser hyperspectral imager and makes use of spatial-spectral correlations by a so-called separability assumption that assumes that the image is made of regions of homogenous spectra. The reconstruction algorithm is simple and ready-to-use and does not require any prior knowledge of the scene. A simple proof-of-principle experiment is performed, demonstrating that only a small number of acquisitions are required, and the resulting compressed data-cube is reconstructed near instantaneously.