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, wherein: the first light channel comprises a first objective lens, a first coded aperture, a first bandpass filter, a first relay lens set, a first prism set, and a first sensor array which are sequentially arranged; the second light channel comprises a second objective lens, a second coded aperture, a second bandpass filter, a second relay lens set, a second prism set, and a second sensor array which are sequentially arranged; the first light beam entering the first light channel is focused and imaged on the first objective lens, the first coded aperture performs random coding for beams on positions of a spectral image; beams of the coded spectral image are filtered by the first bandpass filter, then are relayed by the first relay lens set to the first prism set to produce dispersion; and beams of the dispersed spectral image are sensed by the first sensor array to obtain the first mixing spectral image; and the second light beam is focused and imaged on the second objective lens, the second coded aperture performs random coding for beams on positions of a spectral image; beams of the coded spectral image are filtered by the second bandpass filter, then are relayed by the second relay lens set to the second prism set to produce dispersion; and beams of the dispersed spectral image are sensed by the second sensor array to obtain the second mixing spectral image.