In this paper, two novel multidimensional striping noise compensation (SNC) algorithms for push-broom hyperspectral cameras (PBHCs) have been developed. The SNC algorithms employ a novel pixelwise, affine image-degradation model, which assumes that the striping noise (SN) parameters are spatially uncorrelated, spectrally independent, and decoupled from the camera's spectral response. Algorithms simultaneously exploit the spatial and temporal information contained in an image as well as the spectral information contained at adjacent spectral images. The multidimensional SNC algorithms were successfully tested on real hyperspectral data from both a commercial PBHC operating in the spectral range of 400-1000 nm, at a resolution of 1.04 nm, and the ESA earth-observing CHRIS/PROBA sensor.