Development of computational algorithm for reconstruction of volumetric images in X-ray computed tomography using holographic methods

A computational algorithm for solving the inverse problem of x-ray tomography for reconstruction of the internal structure of micro objects in the near Fresnel zone using holographic methods of visualization of three-dimensional images is considered. Holographic methods do not provide a direct solution to the problem of reconstruction of the internal structure of the object. They can only solve the problem of volumetric display of some object surface. However, using data on the absorption of x-ray radiation of the object and phase-contrast holographic signals in the near Fresnel zone, the possibility of obtaining a three-dimensional holographic image of the inner layers of the object is shown. The solution of this complex problem required the use of three-dimensional (3D) Radon transformation of the internal function of the object and two-dimensional (2D) Radon transformation of phase-contrast holographic projection. An algorithm for reconstruction of phase-contrast tomographic images of the internal structure of the object was obtained and based on it a computational algorithm for the practical reconstruction of three-dimensional tomographic images of the internal structure of micro objects was developed. The results of the research were confirmed by mathematical modeling of the algorithm for reconstruction of three-dimensional images. For this purpose, a mathematical model of the test phantom was developed and phase-contrast projections were simulated for it with subsequent reconstruction of phase-contrast tomographic images by tomographic methods using the program reenactor developed by the authors. A compact algorithm for reconstruction of phase-contrast tomographic images for experimental facilities for the study of small biological objects, when two arrays of measurements are carried out to obtain phase-contrast projections: measurements of brightness from the object on the detector in the near Fresnel zone and measurements from the object on the detector in the absorption zone. The practical application of the developed approach in obtaining phase-contrast tomographic images by tomographic methods can be found for the study of micro objects where high resolution is required in the image than in the application of classical CT methods.