1. A compressive sensing-based multispectral video imager with double channels, comprising: a beamsplitter, a first light channel, a second light channel and an image reconstruction processor, wherein: the beamsplitter is configured to divide the light beam of an underlying image into a first light beam and a second light beam; wherein the first light beam enters the first light channel, and the second light beam enters the second light channel; the first light channel is configured to process and sample the first light beam to obtain a first mixing spectral image and transfer it to the image reconstruction processor; the second light channel is configured to process and sample the second light beam to obtain a second mixing spectral image, and transfer it to the image reconstruction processor; and the image reconstruction processor is configured to reconstruct the underlying spectral image based on the first mixing spectral image and the second mixing spectral image by making use of non-linear optimization method.