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Quasi-random point sequences for compressed sensing: Special session: Low-discrepancy point sets, Invited Talk (G. Larcher & H. Niederreiter) Authors: C. Schretter Publication Date: Jul. 2015
Abstract: 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.
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