title: Noise models for low counting rate coherent diffraction imaging.
abstract: Coherent diffraction imaging (CDI) is a lens-less microscopy method that extracts the complex-valued exit field from intensity measurements alone. It is of particular importance for microscopy imaging with diffraction set-ups where high quality lenses are not available. The inversion scheme allowing the phase retrieval is based on the use of an iterative algorithm. In this work, we address the question of the choice of the iterative process in the case of data corrupted by photon or electron shot noise. Several noise models are presented and further used within two inversion strategies, the ordered subset and the scaled gradient. Based on analytical and numerical analysis together with Monte-Carlo studies, we show that any physical interpretations drawn from a CDI iterative technique require a detailed understanding of the relationship between the noise model and the used inversion method. We observe that iterative algorithms often assume implicitly a noise model. For low counting rates, each noise model behaves differently. Moreover, the used optimization strategy introduces its own artefacts. Based on this analysis, we develop a hybrid strategy which works efficiently in the absence of an informed initial guess. Our work emphasises issues which should be considered carefully when inverting experimental data.
authors.affiliation: Institut Fresnel - Université Aix Marseille, CNRS, Faculté de St Jérôme, 13397 Marseille Cedex 20, France. pierre.godard@fresnel.fr
authors.forename: Pierre
authors.initials: P
authors.lastname: Godard
authors.forename: Marc
authors.initials: M
authors.lastname: Allain
authors.forename: Virginie
authors.initials: V
authors.lastname: Chamard
authors.forename: John
authors.initials: J
authors.lastname: Rodenburg
mesh_terms: D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods; D016013:Likelihood Functions; D008853:Microscopy / Q000379:methods; D015233:Models, Statistical; D008962:Models, Theoretical; D009010:Monte Carlo Method; D016011:Normal Distribution; D055095:Optics and Photonics; D017785:Photons; D010825:Physics / Q000379:methods; D012984:Software; D014961:X-Ray Diffraction / Q000379:methods