Smoothness on rank-order path graphs and its use in compressive spectral imaging with side information

•We introduce the concept of rank-order path graph and show that the rank-order path graph induced by a signal is the indeed the path graph on which the signal is the smoothest.•We derive theoretical properties of rank-order path graphs and illustrate their use in signal recovery from undersampled measurements.•We use smoothness on (approximate) rank-order path graphs to tackle the problem of compressive spectral imaging (CSI) with panchromatic side information.•We provide an experimental demonstration of our approach using a single disperser coded aperture snapshot spectral imaging system.