We present a new image compression scheme for hyperspectral images based on the newly-emerged matrix/tensor completion theory. Unlike typical transform-coding based methods, the proposed approach does not require any transform to be performed by the imaging sensor when doing on-board compression. Only a small set of pixels on a sparse set of locations on the imaging sensor needs to be captured and transmitted for each image. The decoder side relies on matrix/tensor completion for reconstructing the original images. Hence the scheme can drastically reduce the computation and bandwidth requirements on the on-board imaging sensors. Experiments show that the proposed method is able to obtain compression performance close to JPEG2000 while enjoying the afore-mentioned unique benefits.