Methods and systems obtain data representative of a scene across spectral bands using a compressive-sensing-based hyperspectral imaging system comprising optical elements. These methods and systems sample two modes of a three-dimensional tensor corresponding to a hyperspectral representation of the scene using sampling matrices, one for each of the two modes, to generate a modified three-dimensional tensor. After sampling the two modes, such methods and systems sample a third mode of the modified three-dimensional tensor using a third sampling matrix to generate a further modified three-dimensional tensor. Then, the methods and systems reconstruct hyperspectral data from the further modified three-dimensional tensor using the sampling matrices and the third sampling matrix.