Phase retrieval with random Gaussian sensing vectors by alternating projections
Waldspurger, Irène (2018), Phase retrieval with random Gaussian sensing vectors by alternating projections, IEEE Transactions on Information Theory. 10.1109/TIT.2018.2800663
TypeArticle accepté pour publication ou publié
Journal nameIEEE Transactions on Information Theory
IEEE - Institute of Electrical and Electronics Engineers
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We consider a phase retrieval problem, where we want to reconstruct a n-dimensional vector from its phaseless scalar products with m sensing vectors, independently sampled from complex normal distributions. We show that, with a suitable initialization procedure, the classical algorithm of alternating projections (Gerchberg-Saxton) succeeds with high probability when m ≥ Cn, for some C > 0. We conjecture that this result is still true when no special initialization procedure is used, and present numerical experiments that support this conjecture.
Subjects / KeywordsSensors; Convergence; Cost function; Image reconstruction; Phase measurement; Atmospheric measurements; Particle measurements
Showing items related by title and author.
Caprara, Alberto; Furini, Fabio; Lodi, Andrea; Mangia, Mauro; Rovatti, Riccardo; Setti, Gianluca (2014) Article accepté pour publication ou publié