2011/09/30 by F. Krzakala, Florent Krzakala, M. Mézard +7 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Gaussian Processes and Bayesian Inference #Sparse and Compressive Sensing Techniques #cond-mat.stat-mech #cs.IT #math.IT
paper · pdf · doi:10.1103/physrevx.2.021005
published as Phys. Rev. X 2, 021005 (2012) · 20 pages, 8 figures, 3 tables. Related codes and data are available at http://aspics.krzakala.org
openalex publication_date 2012/05/11 · arxiv created 2012/06/06 · arxiv updated 2012/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Compressed sensing has triggered a major evolution in signal acquisition. It consists of sampling a sparse signal at low rate and later using computational power for the exact reconstruction of the signal, so that only the necessary information is measured. Current reconstruction techniques are limited, however, to acquisition rates larger than the true density of the signal. We design a new procedure that is able to reconstruct the signal exactly with a number of measurements that approaches the theoretical limit, i.e., the number of nonzero components of the signal, in the limit of large systems. The design is based on the joint use of three essential ingredients: a probabilistic approach to signal reconstruction, a messagepassing algorithm adapted from belief propagation, and a careful design of the measurement matrix inspired by the theory of crystal nucleation. The performance of this new algorithm is analyzed by statistical-physics methods. The obtained improvement is confirmed by numerical studies of several cases.