This study compares some constructions of low-discrepancy points for image reconstruction from few data samples in compressed sensing. In contrast to Monte Carlo integration, samples are not averaged but their complementary information yields constrains of a large underdetermined linear system. An approximation of the missing information is recovered by solving an ill-posed inverse image reconstruction problem with iterative algorithms. Experiments are conducted on regular images and current research aims towards applying quasi-random constructions for efficient sampling in holographic interference imaging. Results demonstrate potential in using quasi-random sequences for progressive image formation, instead of constructions of sensing matrices using pseudo-random numbers for recovering sparse image approximations with the compressed sensing framework.