1. A method for image reconstruction using a compressed sensing framework for a hyperspectral video system, the method comprising: receiving a plurality of N×N representation matrices, each representation matrix ψ having been constructed for each of a plurality of sub-data cubes each containing a 2D array of pixels, said sub-data cubes collectively comprising a first hyperspectral image data cube constructed from a first set of different spectral planes of a hyperspectral image captured using a reference sensor, where N is the total number of bands in said reference sensor; receiving a M×N sampling matrix Φ comprising a non-square matrix filled with 1's at locations corresponding to the peak wavelengths of filters in a multi-filter grid of a target hyperspectral camera and with remaining elements filled with 0's, where M is the number of bands in said target camera such that M<<N; and using said representation matrices and said sampling matrix to reconstruct a full signal f* of a hyperspectral image captured by said target hyperspectral camera.