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Fourier Inversion of the Mojette Transform [chapter]

Andrew Kingston, Heyang Li, Nicolas Normand, Imants Svalbe
2014 Lecture Notes in Computer Science  
The Mojette transform is a form of discrete Radon transform that maps a 2D image (P ×Q pixels) to a set of I 1D projections.  ...  This paper presents a robust reconstruction method, performed in the Fourier domain, that requires O(P 2 Q log P ) operations.  ...  AK acknowledges l'Univ. de Nantes for funding a one month visit to IVC-IRCCyN where much of this work was undertaken.  ... 
doi:10.1007/978-3-319-09955-2_23 fatcat:bukodg6gwva6nghgh5j366yspe

Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

Shekhar S. Chandra, Nicolas Normand, Andrew Kingston, Jeanpierre Guedon, Imants Svalbe
2014 IEEE Signal Processing Letters  
The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise.  ...  Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation.  ...  INTRODUCTION T HE Discrete Fourier Transform (DFT) is an important tool for various signal processing problems ranging from filtering and convolution to inverse problems, where it is used as a mechanism  ... 
doi:10.1109/lsp.2014.2313341 fatcat:6rk6xr7rijc3dinvr5n64sg6uy

Fast Mojette Transform for Discrete Tomography [article]

Shekhar S. Chandra, Nicolas Normand, Andrew Kingston, Jeanpierre Guédon, Imants Svalbe
2010 arXiv   pre-print
The digital projections are those of the Mojette Transform, a form of discrete linogram.  ...  A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform.  ...  Discrete Tomography Review Discrete reconstruction methods take advantage of digital image geometry of the reconstructions to allow exact inversion schemes.  ... 
arXiv:1006.1965v1 fatcat:5xtvos76aregbhtj2gxfgcrmie

Some links between continuous and discrete Radon transform

Myriam C. J. Servieres, Nicolas Normand, Peggy Subirats, JeanPierre Guedon, J. Michael Fitzpatrick, Milan Sonka
2004 Medical Imaging 2004: Image Processing  
Fourier transform of a trapezoidal shape.  ...  Here we obtain a novel version of the Spline 0 FBP algorithm with a complete continuous/discrete correspondence using a specific discrete Radon transform, the Mojette transform.  ...  The pixel size is unitary. The inverse fourier transform of (Eq.??)  ... 
doi:10.1117/12.533472 dblp:conf/miip/ServieresNSG04 fatcat:upnbtjvhkjahjkkg7azrfuxgee

Parallel-Beam CT Reconstruction Based on Mojette Transform and Compressed Sensing

Wen Hou, Cishen Zhang
2013 International Journal of Computer and Electrical Engineering  
Then 1D Fourier transform is applied to the modified Mojette projections, followed by an exact mapping of the gained Fourier coefficients to the 2D Fourier domain of the scanning object.  ...  A novel frame of parallel-beam Computerized Tomography (CT) reconstruction is proposed. The CT projections are firstly converted to Mojette projections.  ...  and Mift applies direct inverse Fourier transform to the Mojette projections.  ... 
doi:10.7763/ijcee.2013.v5.669 fatcat:ph2ul66gv5gn5nzxlukkkwm57m

The Mojette Transform: The First Ten Years [chapter]

JeanPierre Guédon, Nicolas Normand
2005 Lecture Notes in Computer Science  
In this paper the Mojette transforms class is described. After recalling the birth of the Mojette transform, the Dirac Mojette transform is recalled with its basic properties.  ...  After recalling the birth of the Mojette transform, the Dirac Mojette transform is recalled with its basic properties.  ...  Acknowledgements The authors would like to thank Jean-Marc Chassery for his indefectible help to promote the Mojette transform andÉric Andres and the DGCI board for their kind invitation to write this  ... 
doi:10.1007/978-3-540-31965-8_8 fatcat:n2rbgkhf6ncbdkieebykxyiiuu

Angular assessment of the Mojette filtered back projection

Peggy Subirats, Myriam C. J. Servieres, Nicolas Normand, JeanPierre Guedon, J. Michael Fitzpatrick, Milan Sonka
2004 Medical Imaging 2004: Image Processing  
For this, we use a version of the discrete exact Radon transform called the Mojette transform that has been developed in our team for few years.  ...  Because of the discrete set of angles used in the FBP algorithm, discrete angles issued from Farey's series were used. Our version of the FBP algorithm is compared with the classical FBP algorithm.  ...  The algorithm complexity of both the direct and inverse Mojette transform is O(IN ) where N is the number of pixels.  ... 
doi:10.1117/12.533483 dblp:conf/miip/SubiratsSNG04 fatcat:nrbhzu6psfaydhxj3vokhm2tgi

A Geometry Driven Reconstruction Algorithm for the Mojette Transform [chapter]

Nicolas Normand, Andrew Kingston, Pierre Évenou
2006 Lecture Notes in Computer Science  
The Mojette transform is an entirely discrete form of the Radon transform developed in 1995.  ...  The Mojette transform is an entirely discrete form of the Radon transform developed in 1995.  ...  Acknowledgements AK holds a postdoctoral position at l'Université de Nantes supported by a grant from the Région Pays de la Loire, France.  ... 
doi:10.1007/11907350_11 fatcat:a4kk4xrotba2hmqiypm3cood7q

Lossless Image Compression and Selective Encryption using a Discrete Radon Transform

A. Kingston, S. Colosimo, P. Campisi, F. Autrusseau
2007 2007 IEEE International Conference on Image Processing  
Besides the compression capabilities, the Mojette transforms brings an interesting property: a tunable redundancy.  ...  The discrete Radon projections investigated here are those used to define the Mojette transform first presented by Gué don et al.  ...  Acknowledgements The majority of this work was conducted while A.K. held a postdoctoral position at l'Université de Nantes supported by a grant from the Ré gion Pays de la Loire, France.  ... 
doi:10.1109/icip.2007.4380055 dblp:conf/icip/KingstonCCA07 fatcat:cggjyu2u4bcaji2o67qnoiymli

Noise Robust Mojette Reconstructions for Missing Wedge Effect Attenuation

Benoit Recur, Pascal Desbarats, Jean-Philippe Domenger
2010 Journal of Multimedia Processing and Technologies  
The Mojette transform is a tomographic reconstruction method based on a discrete and finite interpretation of the Radon theorem.  ...  Since the Mojette acquisition follows the discrete image geometry, this method resolves the wellknown irregular sampling problem.  ...  Mojette Transform The Dirac-Mojette transform [8] , [7] , [6] is defined as a discrete version of the Radon transform.  ... 
dblp:journals/jmpt/RecurDD10 fatcat:pzgryqqizbcpji4j6pjy6ykdta

Lossless image compression via predictive coding of discrete Radon projections

Andrew Kingston, Florent Autrusseau
2008 Signal processing. Image communication  
Besides the compression capabilities, the Mojette transforms brings an interesting property: a tunable redundancy.  ...  The 1D Mojette projections are re-arranged as two dimensions images, thus allowing the use of 2D image compression techniques onto the projections.  ...  Acknowledgements The majority of this work was conducted while AK held a postdoctoral position at l'Université de Nantes supported by a grant from the Région Pays de la Loire, France.  ... 
doi:10.1016/j.image.2008.03.001 fatcat:kicuk2mqszd5tbngvmmev4duku

The discrete Radon transform: a more efficient approach to image reconstruction?

Andrew Kingston, Imants Svalbe, Jean-Pierre Guédon, Stuart R. Stock
2008 Developments in X-Ray Tomography VI  
The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0, π).  ...  Alternatively, a discrete Radon transform (DRT) and its inversion can be implemented.  ...  To date the Mojette transform has no fast well-conditioned inversion.  ... 
doi:10.1117/12.795779 fatcat:duy3dsovafbwhgt6sxexrxduee

Secured and progressive transmission of compressed images on the Internet: application to telemedicine

Marie Babel, Benoit Parrein, Olivier Deforges, Nicolas Normand, Jean-Pierre Guedon, Joseph Ronsin, Simone Santini, Raimondo Schettini, Theo Gevers
2005 Internet Imaging VI  
For this purpose, we present in this paper an original scalable image compression technique (LAR method) used in association with a channel coding method based on the Mojette Transform, so that a hierarchical  ...  Within the framework of telemedicine, the amount of images leads first to use efficient lossless compression methods for the aim of storing information.  ...  The Mojette transform is linear with the pixels number and the projections number, as the Fourier and Meyer (wavelet) ones.  ... 
doi:10.1117/12.589191 fatcat:zpj34d4o5vbldo7lzshxk4wi2q

Joint source–channel coding: Secured and progressive transmission of compressed medical images on the Internet

Marie Babel, Benoît Parrein, Olivier Déforges, Nicolas Normand, Jean-Pierre Guédon, Véronique Coat
2008 Computerized Medical Imaging and Graphics  
In this context, the use of scalable coding, Locally Adapted Resolution (LAR) and a discrete and exact Radon transform, known as the Mojette transform, meets this twofold requirement.  ...  image and the properties of a network with no guaranteed quality of service.  ...  the Fourier and Meyer (wavelet) transforms.  ... 
doi:10.1016/j.compmedimag.2008.01.002 pmid:18289830 fatcat:uuql3hody5dihbfsjcbazjrxi4

Central and Periodic Multi-Scale Discrete Radon Transforms

Óscar Gómez-Cárdenes, José G. Marichal-Hernández, Jonas Phillip Lüke, José M. Rodríguez-Ramos
2021 Applied Sciences  
Central DRT can provide almost a 2× speedup over conventional DRT, probably becoming the faster Radon transform algorithm available, at the cost of ignoring 15% of the summations in the corners.  ...  Both have an output of size N×4N, instead of 3N×4N, as in the original algorithm. Periodic DRT is proven to have a fast inversion, whereas central DRT does not.  ...  , the fast Mojette transform, FMT.  ... 
doi:10.3390/app112210606 fatcat:shm4glttqvgr5g63722fty35v4
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