Deterministic versus stochastic level-set regularization in nonlinear phase contrast tomography. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Sixou, Bruno
• Is Part Of: Inverse problems in science and engineering. Volume 25:Issue 6(2017)
• Page Start: 810
• Page End: 831
• Publication Date: 2017-06-03
• Subjects: Inverse problems -- phase constrast tomography -- X-ray imaging; 65J22 -- 65J20 -- 65K10; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2016.1201662
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : A new nonlinear level-set regularization method to reconstruct the complex refractive index distribution with in-line phase contrast tomography measurements is presented under the assumption that the index is piecewise constant. The nonlinear iterative approach is based on the Fréchet derivative of the intensity recorded at a single propagation distance and for several projection angles. The algorithm is successfully applied to a multi-material object for several noise levels. Better reconstruction results are achieved with a stochastic perturbation of the level-set function. This evolution corresponds to a stochastic evolution of the shape of the reconstructed regions. The reconstruction errors can be further decreased with topological derivatives. The different algorithms are tested on various multi-material objects.