21 June 2015 Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures
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Abstract
Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography – Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.
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W. Krauze, W. Krauze, P. Makowski, P. Makowski, M. Kujawińska, M. Kujawińska, } "Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260Y (21 June 2015); doi: 10.1117/12.2184830; https://doi.org/10.1117/12.2184830
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