{"version":1,"kind":"Article","sha256":"","slug":"177","location":"","dependencies":[],"doi":"10.54294/z83ly1","thumbnail":"https://pub.desci.com/ipfs/bafkreiaxugcihnbufp5k5plu466ifxbcy7pledxqsphothgnzq64hzxpxy","frontmatter":{"title":"Direct Fourier Tomographic Reconstruction Image-To-Image Filter","abstract":"We present an open-source ITK implementation of a direct Fourier method for tomographic reconstruction, applicable to parallel-beam x-ray images. Direct Fourier reconstruction makes use of the central-slice theorem to build a polar 2D Fourier space from the 1D transformed projections of the scanned object, that is resampled into a Cartesian grid. Inverse 2D Fourier transform eventually yields the reconstructed image. Additionally, we provide a complex wrapper to the BSplineInterpolateImageFunction to overcome ITK’s current lack for image interpolators dealing with complex data types. A sample application is presented and extensively illustrated on the Shepp-Logan head phantom. We show that appropriate input zeropadding and 2D-DFT oversampling rates together with radial cubic b-spline interpolation improve 2D-DFT interpolation quality and are efficient remedies to reduce reconstruction artifacts.","license":"You are licensing your work to Kitware Inc. under the\nCreative Commons Attribution License Version 3.0.\n\nKitware Inc. agrees to the following:\n\nKitware is free\n * to copy, distribute, display, and perform the work\n * to make derivative works\n * to make commercial use of the work\n\nUnder the following conditions:\n\\\"by Attribution\\\" - Kitware must attribute the work in the manner specified by the author or licensor.\n\n * For any reuse or distribution, they must make clear to others the license terms of this work.\n * Any of these conditions can be waived if they get permission from the copyright holder.\n\nYour fair use and other rights are in no way affected by the above.\n\nThis is a human-readable summary of the Legal Code (the full license) available at\nhttp://creativecommons.org/licenses/by/3.0/legalcode","keywords":["CT","Direct Fourier Method","Tomographic Reconstruction","Image-To-Image Filter"],"authors":[{"name":"Zosso, Dominique","email":"dominique.zosso@epfl.ch","affiliations":["EPFL Signal Processing Institute"],"corresponding":true},{"name":"Bach Cuadra, Meritxell","affiliations":[]},{"name":"Thiran, Jean-Philippe","affiliations":[]}],"date_submitted":"2007-08-24T10:21:19Z","external_publication_id":177,"revision_cids":["bafkreiexj2sdbznpeq272x4gjjcaiivdwn4ioqi5jyrmk222mq2crb4p6m"],"thumbnail":"https://pub.desci.com/ipfs/bafkreiaxugcihnbufp5k5plu466ifxbcy7pledxqsphothgnzq64hzxpxy"},"mdast":{"type":"root"},"downloads":[{"url":"https://pub.desci.com/ipfs/bafkreihmzorh4lu77xtl5z7kfcw5zz2z3fwifatmtoeliingj66amc72xa","title":"root/code/CMakeLists.txt","filename":"CMakeLists.txt","extra":{"size_bytes":2036,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiez47jakaqslt5ehj7xc637jbskn2bhu72ernyuj3ap7hmyttqhxm","title":"root/code/DirectFourierReconstruct.cxx","filename":"DirectFourierReconstruct.cxx","extra":{"size_bytes":4595,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreieunevs3itdf5kdfyy7xh3ee3pswxp3d2ej76an43gmg4oxi5dycu","title":"root/code/itkComplexBSplineInterpolateImageFunction.h","filename":"itkComplexBSplineInterpolateImageFunction.h","extra":{"size_bytes":4788,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreig3oiilidcd6eb4t6bcxlcfgfomtgctsfgg6qh4m24cbb5am4xhim","title":"root/code/itkComplexBSplineInterpolateImageFunction.txx","filename":"itkComplexBSplineInterpolateImageFunction.txx","extra":{"size_bytes":2704,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreibfwzufkjdj2s4yp5xxklymn2ceh7lx77ilzamptzrwxnhkxhikru","title":"root/code/itkDirectFourierReconstructionImageToImageFilter.h","filename":"itkDirectFourierReconstructionImageToImageFilter.h","extra":{"size_bytes":5899,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreidmwdf5u3fvh3z3cn33nnozyk6hutxb4rdpxpna6fgn53o5yjhofu","title":"root/code/itkDirectFourierReconstructionImageToImageFilter.txx","filename":"itkDirectFourierReconstructionImageToImageFilter.txx","extra":{"size_bytes":13764,"type":"file"}},{"url":"https://ipfs.desci.com/ipfs/bafkreifn7vj6tcgjssx2ktdcpdowtdsf4pt2ounqu3qyfsfnfjpxe5onuq","title":"root/insight-journal-metadata.json","filename":"insight-journal-metadata.json","extra":{"size_bytes":5144,"type":"file"}},{"url":"https://dweb.link/ipfs/bafybeidfghyy4cpyzqkjqwgu64bpq2vh2z5ygvuz55xvqw4nrqlpqtoqay","title":"root/article.pdf","filename":"article.pdf","extra":{"size_bytes":5217987,"type":"file"}}],"references":{"cite":{"order":["ref1","ref2","ref3","ref4","ref5","ref6"]},"data":{"ref1":{"label":"ref1","enumerator":"1","url":"https://doi.org/10.1109/42.845180","html":"´n. On the Direct Fourier Method for Computer Tomography+IEEE Transactions on Medical Imaging+19+3+223+232+2000+D. Gottlieb+B. Gustafsson+P. Forsse"},"ref2":{"label":"ref2","enumerator":"2","html":"In Proceedings of the IEEE+71+390+408+1983+R. M. Lewitt"},"ref3":{"label":"ref3","enumerator":"3","url":"https://doi.org/10.1109/nssmic.1992.301056","html":"Artefacts and Remedies in Direct Fourier Tomographic Reconstruction. Nuclear Science Symposium and Medical Imaging Conference+1+2+1140+1992+M. Magnusson+P. Edholm"},"ref4":{"label":"ref4","enumerator":"4","url":"https://doi.org/10.1109/tns.1974.6499235","html":"The Fourier reconstruction of a head section+IEEE Transactions on Nuclear Science+4+2+43+1974+L. A. Shepp+B. F. Logan"},"ref5":{"label":"ref5","enumerator":"5","url":"https://doi.org/10.1364/josa.69.001519","html":"Sampling theorems in polar coordinates+Journal of the Optical Society of America+4+11+2+1525+1979+H. Stark"},"ref6":{"label":"ref6","enumerator":"6","url":"https://doi.org/10.1109/tassp.1981.1163528","html":"Direct Fourier reconstruction in computer tomography+IEEE Transactions on Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing]+29+2+1+245+April 1981+H. Stark+J. Woods+R. Hingorani"}}}}