A reconstruction matrix used for calculating a hyperspectral data-cube includes rows of periodic functions. Each row of the reconstruction matrix corresponds to a selected wavelength and each column corresponds to a selected retardance of an interferometer. The periodic functions have as a parameter the selected wavelength of the corresponding row and are sampled at the selected retardances of each of the corresponding columns. An interferogram data-cube is obtained and includes an array of one or more simultaneously measured interferograms. Each row of the interferogram data-cube corresponds to one of the selected retardances and each column corresponds to a different interferogram from the simultaneously measured interferograms. A set of matrix-vector products for each of the interferograms is formed by multiplying the reconstruction matrix with a column of the interferogram data-cube to form the hyperspectral data-cube.