A new pseudorandom coded aperture design framework for multi-frame Coded Aperture Snapshot Spectral Imaging (CASSI) system is presented. Our previous work determines a matrix system model for multi-frame CASSI which is used to design sets of spectrally selective coded apertures. Then, the required number of CASSI measurements is dictated by the desired profile of spectral bands. This work aims at optimizing the set of selective coded apertures such that the number of FPA CASSI measurements is reduced to a desired number of shots, regardless of the targeted spectral profile. A set of pseudorandom weights are determined such that the rank of the matrix representing the ensemble of weighted spectrally selective coded apertures is optimized. Simulations show higher quality of spectral image reconstruction than those attained by systems using random coded aperture sets.