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Comparison of parabolic filtration methods for 3D filtered back projection in pulsed EPR imaging

Zhiwei Qiao, Gage Redler, Boris Epel, Howard J. Halpern
2014 Journal of magnetic resonance (San Diego, Calif. 1997 : Print)  
For 3D tomographic EPRI, the most commonly used reconstruction algorithm is filtered back projection (FBP), in which the parabolic filtration process strongly influences image quality.  ...  In the presence of noise, the 3 point derivative method and Hamming-window parabolic filtration method resulted in the best compromise between low image noise and high spatial resolution.  ...  (8) From the inverse FT, we obtain the UIR: (9) Letting t = nd, we obtain the discrete UIR shown in Eq. (10).  ... 
doi:10.1016/j.jmr.2014.08.010 pmid:25314081 pmcid:PMC4324566 fatcat:5j6y5znmnfh7pa237ml7i5mn7u

Sliced Ridgelet Transform for Image Denoising

V.Krishna Naik
2013 IOSR Journal of Computer Engineering  
Then, the inverse ridgelet transform is computed to get back the denoised version of that projection of slice at the same angle.  ...  The projection of image at a certain angle is computed at a certain angle, but only on a defined slice of the noisy image.  ...  The filtered back projection algorithm is split into two phases, filtration and projection.  ... 
doi:10.9790/0661-1411721 fatcat:laxw4so7ybcyfckt7axg5re7ji

Simulating point processes by intensity projection

Kay Giesecke, Hossein Kakavand, Mohammad Mousavi
2008 2008 Winter Simulation Conference  
However, discretization introduces bias into the simulation results. This paper proposes a method for the exact simulation of point processes with stochastic intensities.  ...  They can be simulated from standard Poisson arrivals by time-scaling with the cumulative intensity, whose path is typically generated with a discretization method.  ...  natural filtration of H is given by the optional projection of λ onto the natural filtration of N.  ... 
doi:10.1109/wsc.2008.4736114 dblp:conf/wsc/GieseckeKM08 fatcat:cos3dztrwfcj7fvxqb7sz5zrde

Simulating Point Processes by Intensity Projection

Kay Giesecke, Hossein Kakavand, Mohammad Hossein Mousavi
2008 Social Science Research Network  
However, discretization introduces bias into the simulation results. This paper proposes a method for the exact simulation of point processes with stochastic intensities.  ...  They can be simulated from standard Poisson arrivals by time-scaling with the cumulative intensity, whose path is typically generated with a discretization method.  ...  natural filtration of H is given by the optional projection of λ onto the natural filtration of N.  ... 
doi:10.2139/ssrn.1159473 fatcat:ahwqxa5gknfkpaao3ykhj7ii6i

Fast computation of 3D radon transform via a direct Fourier method

S. Lanzavecchia, P. Luigi Bellon
1998 Bioinformatics  
The Radon transform can be implied in their manipulation mainly for the solution of the inverse tomographic problem, since experimental data are often collected as projections or as samples of the Radon  ...  The times required to compute a number of projections with use of the Radon transform are compared with those required by other algorithms.  ...  Acknowledgements This work has been financed by the Italian Ministry of University and Research (40% and 60%) and by the National Research Council of Italy.  ... 
doi:10.1093/bioinformatics/14.2.212 pmid:9545454 fatcat:sn5ue4qwi5apnpwnmv7kowk2yq

Backprojection inverse filtration for laminographic reconstruction

Thomas Blumensath
2018 IET Image Processing  
They use interpolation and backprojection techniques to generate an initial estimate of an object's internal structure using projection images taken at different orientations.  ...  Depending on the scanning geometry used to calculate the tomographic projections, this initial estimate can be understood as a blurred (filtered) approximation of the actual structure.  ...  Acknowledgments This research was supported by Innovate UK grant 101804, EPSRC grant EP/K037102/1 and through a Faculty of Engineering and the Environment funded New Frontiers Fellowship.  ... 
doi:10.1049/iet-ipr.2017.1344 fatcat:a4dbqcbt6zb65a35pvpd4sfry4

A Fast Imaging Technique Applied to 2D Electrical Resistivity Data

Raffaele Martorana, Patrizia Capizzi
2014 International Journal of Geophysics  
Finally, two field cases are discussed and the comparison between back-projection and inversion is shown.  ...  In the past some modifications to the back-projection algorithm, as well as the use of filtering techniques for the sensitivity matrix were proposed.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/846024 fatcat:7tfu333rfndwlduwpsnf6vz2iu

Projective Transforms on Periodic Discrete Image Arrays [chapter]

Andrew Kingston, Imants Svalbe
2006 Advances in Imaging and Electron Physics  
The authors would like to thank Professor Jean-Pierre Guédon and the Mojette team fromÉcole polytechnique de l'Université de Nantes, for their input on the applications of redundancy in projections.  ...  on the mathematical properties of the FRT.  ...  Exact inversion is possible via Fourier inversion or a form of back-projection (2).  ... 
doi:10.1016/s1076-5670(05)39002-1 fatcat:cvmnle3jqjaktkz2p7sl75njtu

Image reconstruction for a general circle-plus trajectory

A Katsevich
2007 Inverse Problems  
Back projection-filtration (BPF) algorithms are very flexible and can be easily derived for almost any scanning curve described in T. Zhuang, S. Leng, B. E. Nett, G.  ...  Chen, New families of exact fan-beam and cone-beam image reconstruction formulae via 65 filtering the back projection image of differentiated projection data along singly measured lines, Inverse Problems  ...  II and select a discrete set of lines tangent to a convex hull of that projection. 12.  ... 
doi:10.1088/0266-5611/23/5/024 fatcat:c4ow3ivpubgv3pekgmajcz6fqy

Harmonic Analysis over adelic spaces [article]

Anton Deitmar
2007 arXiv   pre-print
Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring.  ...  We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation formula for all dimensions.  ...  Dually we define the notion of discrete objects. Every object of S 0 is discrete.  ... 
arXiv:0708.0322v5 fatcat:isclh4jj6fexta3cveouoshrq4

Sart-Type Half-Threshold Filtering Approach for CT Reconstruction

Hengyong Yu, Ge Wang
2014 IEEE Access  
In the medical imaging filed, the discrete gradient transform (DGT) is widely used to define the sparsity.  ...  They are complementary to the counterparts of the state-of-the-art softthreshold filtering and hard-threshold filtering.  ...  While the whole matrix A represents the forward projection, A T implements the back projection. B.  ... 
doi:10.1109/access.2014.2326165 pmid:25530928 pmcid:PMC4269945 fatcat:lzmkw2522jcjhbhzgqkzyvlvv4

Space-Filling X-Ray Source Trajectories for Efficient Scanning in Large-Angle Cone-Beam Computed Tomography

Andrew M. Kingston, Glenn R. Myers, Shane J. Latham, Benoit Recur, Heyang Li, Adrian P. Sheppard
2018 IEEE Transactions on Computational Imaging  
of mutually independent data, and third, an improved condition number of the tomographic inverse problem.  ...  ., circles, saddles, or helices, with a large degree of redundant information in adjacent projection images.  ...  The authors would also like to thank the use of supercomputer time provided by Australias National Computational Infrastructure.  ... 
doi:10.1109/tci.2018.2841202 fatcat:7djwewskrnfl3gmtxgz7ktmhju

Fundamentals of Three-Dimensional Reconstruction from Projections [chapter]

Pawel A. Penczek
2010 Methods in Enzymology  
The problem is interesting in that in its discrete form it is ill-posed and not invertible.  ...  Various algorithms have been proposed to cope with the practical difficulties of this inversion problem and their differ widely in terms of their robustness with respect to noise in the data, completeness  ...  Acknowledgments I thank Grant Jensen, Justus Loerke, and Jia Fang for critical reading of the manuscript and for helpful suggestions.  ... 
doi:10.1016/s0076-6879(10)82001-4 pmid:20888956 pmcid:PMC3165033 fatcat:qsuvwlofl5gpfkxiuuf7asi2du

Filtrations on algebraic cycles and homology

Eric M. Friedlander
1995 Annales Scientifiques de l'Ecole Normale Supérieure  
Nori's filtration {AkCHr{X)} on the (discrete) group of algebraic r-cycles on a projective, smooth variety X is defined as follows: AkCHr{X) C Zr(X) is the subgroup generated by those cycles rationally  ...  The commutativity of the left squares follow 4° sfiRffi -TOME 28 -1995 -N° 3 FILTRATIONS ON ALGEBRAIC CYCLES AND HOMOLOGY 323 from the naturality of the push-forward (for proper maps) and pull-back (for  ... 
doi:10.24033/asens.1716 fatcat:am6vyj4ftrhpnlt7mylkeni3au

Topological tensor representations of gl(V) for a space V of countable dimension [article]

Francesco Esposito, Ivan Penkov
2022 arXiv   pre-print
The Lie algebra gl(V) is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space V.  ...  We define a tensor category of topological representations of the Lie algebra gl(V), so that V, its dual and the adjoint representation gl(V) are objects of this category.  ...  Let now Z = lim ← − Z/Z (i) be a presentation of the pro-discrete vector space Z as the projective limit of the discrete spaces Z/Z (i) .  ... 
arXiv:2206.00654v1 fatcat:w53msqivw5dzddylr2jivj6cd4
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