INVERSION OF ELECTRON TOMOGRAPHY IMAGES USING L 2 -GRADIENT FLOWS —- COMPUTATIONAL METHODS *

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L 2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

[1]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[2]  E. Cheney.  Introduction to approximation theory , 1966 .

[3]  Gabor T. Herman,et al.  Algorithms for Three-dimensional Reconstruction From the Imperfect Projection Data Provided by Electron Microscopy , 2007 .

[4]  Gabor T. Herman,et al.  Image reconstruction from projections : the fundamentals of computerized tomography , 1980 .

[5]  Joachim Frank,et al.  Introduction: Principles of Electron Tomography , 2007 .

[6]  Pierre Kornprobst,et al.  Mathematical problems in image processing - partial differential equations and the calculus of variations , 2010, Applied mathematical sciences.

[7]  M. Radermacher.  Weighted Back-Projection Methods , 2007 .

[8]  G. Sapiro,et al.  Geometric partial differential equations and image analysis [Book Reviews] , 2001, IEEE Transactions on Medical Imaging.

[9]  P. Gilbert.  Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.

[10]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[11]  Chandrajit L. Bajaj,et al.  Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction , 2008, Journal of Computer Science and Technology.

[12]  L. Evans.  Measure theory and fine properties of functions , 1992 .

[13]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[14]  X. Guoliang,et al.  PROGRESSIVE COMPUTATION AND NUMERICAL TABLES OF GENERALIZED GAUSSIAN QUADRATURE FORMULAS , 2006 .

[15]  Duccio Fanelli,et al.  Electron tomography: a short overview with an emphasis on the absorption potential model for the forward problem , 2008 .

[16]  G. Sapiro,et al.  Molecular architecture of native HIV-1 gp120 trimers , 2008, Nature.

[17]  Donald Bliss,et al.  Cryoelectron Tomographic Analysis of an HIV-neutralizing Protein and Its Complex with Native Viral gp120* , 2007, Journal of Biological Chemistry.

[18]  Abraham J. Koster,et al.  Cryotomography: Low-dose Automated Tomography of Frozen-hydrated Specimens , 2007 .

[19]  J M Carazo,et al.  XMIPP: a new generation of an open-source image processing package for electron microscopy. , 2004, Journal of structural biology.