C-library raft: Reconstruction algorithms for tomography. Applications to X-ray fluorescence tomography

Abstract There are many reconstruction algorithms for tomography, raft for short, and some of them are considered “classic” by researchers. The so-called raft library, provide a set of useful and basic tools, usually needed in many inverse problems that are related to medical imaging. The subroutines in raft are free software and written in C language; portable to any system with a working C compiler. This paper presents source codes written according to raft routines, applied to a new imaging modality called X-ray fluorescence tomography. Program summary Program title: raft Catalogue identifier: AEJY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJY_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence, version 2 No. of lines in distributed program, including test data, etc.: 218 844 No. of bytes in distributed program, including test data, etc.: 3 562 902 Distribution format: tar.gz Programming language: Standard C. Computer: Any with a standard C compiler Operating system: Linux and Windows Classification: 2.4, 2.9, 3, 4.3, 4.7 External routines: raft: autoconf 2.60 or later – http://www.gnu.org/software/autoconf/ GSL scientific library – http://www.gnu.org/software/gsl/ Confuse parser library – http://www.nongnu.org/confuse/ raft-fun: gengetopt – http://www.gnu.org/software/gengetopt/gengetopt.html Nature of problem: Reconstruction algorithms for tomography, specially in X-ray fluorescence tomography. Solution method: As a library, raft covers the standard reconstruction algorithms like filtered backprojection, Novikovʼs inversion, Hoganʼs formula, among others. The input data set is represented by a complete sinogram covering a determined angular range. Users are allowed to set solid angle range for fluorescence emission at each algorithm. Running time: 1 second to 15 minutes, depending on the data size.

[1]  Frank Natterer,et al.  Mathematical methods in image reconstruction , 2001, SIAM monographs on mathematical modeling and computation.

[2]  J Guy,et al.  Solutions for Fredholm equations through nonlinear iterative processes , 1984 .

[3]  L. Jarczyk,et al.  Elemental composition of the human atherosclerotic artery wall , 2004, Histochemistry.

[4]  Tetsuya Yuasa,et al.  Reconstruction method for fluorescent X-ray computed tomography by least-squares method using singular value decomposition , 1997 .

[5]  M. Chukalina,et al.  Internal elemental microanalysis combining x-ray fluorescence, Compton and transmission tomography , 2003 .

[6]  Anil K. Jain Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[7]  R. Novikov An inversion formula for the attenuated X-ray transformation , 2002 .

[8]  J. Fessler Statistical Image Reconstruction Methods for Transmission Tomography , 2000 .

[9]  S. Deans The Radon Transform and Some of Its Applications , 1983 .

[10]  Alvaro R. De Pierro,et al.  Fluorescence tomography: Reconstruction by iterative methods , 2008, 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[11]  Alvaro R. De Pierro,et al.  Iterative Reconstruction in X-ray Fluorescence Tomography Based on Radon Inversion , 2011, IEEE Transactions on Medical Imaging.

[12]  J. Weigelt,et al.  X-ray fluorescent computer tomography with synchrotron radiation , 1998 .

[13]  P. A. Lay,et al.  High resolution nuclear and X-ray microprobes and their applications in single cell analysis , 2001 .

[14]  R. Gonsalves,et al.  Fluorescent computer tomography: a model for correction of X-ray absorption , 1991 .

[15]  Athanassios S. Fokas,et al.  A Unified Approach To Boundary Value Problems , 2008 .

[16]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

[18]  L. Kunyansky Generalized and attenuated radon transforms: restorative approach to the numerical inversion , 1992 .

[19]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[20]  Bruno Golosio,et al.  Software for x-ray fluorescence and scattering tomographic reconstruction , 2001 .

[21]  Lee-Tzuu Chang,et al.  A Method for Attenuation Correction in Radionuclide Computed Tomography , 1978, IEEE Transactions on Nuclear Science.

[22]  E. Miqueles,et al.  Exact analytic reconstruction in x-ray fluorescence CT and approximated versions , 2010, Physics in medicine and biology.

[24]  M. Newville,et al.  Reduced-Scan Schemes for X-Ray Fluorescence Computed Tomography , 2007, IEEE Transactions on Nuclear Science.

[25]  Leonid Kunyansky A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula , 2001 .

[26]  Alvaro R. De Pierro,et al.  A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography , 1995, IEEE Trans. Medical Imaging.