%0 Journal Article %T Inline hologram reconstruction with sparsity constraints %+ Laboratoire Hubert Curien (LHC) %+ Institute for Analysis and Algebra %+ Centre de Recherche Astrophysique de Lyon (CRAL) %+ Center for Industrial Mathematics %A Denis, Loïc %A Lorenz, Dirk %A Thiébaut, Éric %A Fournier, Corinne %A Trede, Dennis %< avec comité de lecture %@ 0146-9592 %J Optics Letters %I Optical Society of America - OSA Publishing %V 34 %N 22 %P 3475 %8 2009-11-15 %D 2009 %R 10.1364/OL.34.003475 %Z Engineering Sciences [physics]/Signal and Image processing %Z Computer Science [cs]/Signal and Image ProcessingJournal articles %X Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin-images. When objects located at different depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this letter, we consider inverting the hologram formation model in Bayesian framework. We suggest the use of a sparsity-promoting prior, intrinsically verified due to inline holography requirements, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising. %G English %2 https://ujm.hal.science/ujm-00397994v2/document %2 https://ujm.hal.science/ujm-00397994v2/file/OL_sparse_reconstruction_DH_revised_2line.pdf %L ujm-00397994 %U https://ujm.hal.science/ujm-00397994 %~ UNIV-ST-ETIENNE %~ ENS-LYON %~ INSU %~ IOGS %~ CNRS %~ UNIV-LYON1 %~ LAHC %~ PRUNEL %~ PARISTECH %~ CRAL %~ UDL %~ UNIV-LYON