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SPECTRAL PROPERTIES OF PROJECTION SIGNALS IN 3-D TOMOGRAPHY

Yingbo Li, Anton Kummert, Fritz Boschen, Hans Herzog
2005 IFAC Proceedings Volumes  
On the basis of this result, an optimal interleaved sampling pattern is established.  ...  In this paper the spectral properties of two different types of projection signals appearing in 3-D tomography are considered.  ...  It is shown that an optimal interleaved sampling grid in 3-D space requires only one-fourth of sampling points compared to the commonly used progressive sampling grids.  ... 
doi:10.3182/20050703-6-cz-1902.00183 fatcat:u7u7hn472fhpvcbk3lvyv4z6l4

A surprising Radon transform result and its application to motion detection

T.L. Marzetta, L.A. Shepp
1999 IEEE Transactions on Image Processing  
For an ellipse (and its special cases, the disk and the linesegment) the special Radon transform property of the ellipse enables us to obtain a closed-form, analytical solution for the minimax filter,  ...  We prove that this peculiar property is unique to the ellipse; no other convex, compact region of the plane supports a nonzero-valued function whose Radon transform depends only on slope.  ...  ACKNOWLEDGMENT The authors would like to thank R. Burridge, P. C. Fishburn, L. Flatto, and T. J. Richardson for their helpful comments during this research.  ... 
doi:10.1109/83.777085 pmid:18267519 fatcat:xklalupd25h3dcmhf2n3vmquly

Wavelet Sampling and Localization Schemes for the Radon Transform in Two Dimensions

Ge Wang, Grant Welland, Shiying Zhao
1997 SIAM Journal on Applied Mathematics  
Two theorems are presented for wavelet decompositions of the two-dimensional Radon transform.  ...  These results show how to design a multilevel sampling and localization strategy for parallel-beam scanning by using wavelet regularity and vanishing moment characteristics, clarify the interaction between  ...  We are grateful to the referee for many valuable comments on the first version of this paper. The first author was partially supported by the Summer Research Fellowship, University of Missouri-St.  ... 
doi:10.1137/s0036139995290575 fatcat:rxyo45t5ufg5rpf2gpa6yw3eg4

A Box Spline Calculus for the Discretization of Computed Tomography Reconstruction Problems

A. Entezari, M. Nilchian, M. Unser
2012 IEEE Transactions on Medical Imaging  
In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms.  ...  In particular, we prove that the 2-D Radon transform of an -direction box spline is generally a (nonuniform) polynomial spline of degree .  ...  efficiency of the Cartesian lattice due to their densest spectral packing properties.  ... 
doi:10.1109/tmi.2012.2191417 pmid:22453611 fatcat:bnotv4enhrau5l5u73aj3xjanu

Fully automatic classification of breast cancer microarray images

Nastaran Dehghan Khalilabad, Hamid Hassanpour, Mohammad Reza Abbaszadegan
2016 Journal of Electrical Systems and Information Technology  
A microarray image is used as an accurate method for diagnosis of cancerous diseases. The aim of this research is to provide an approach for detection of breast cancer type.  ...  Then, by the sum of the pixels associated with each gene, the amount of "genes expression" is extracted as raw data.  ...  Microarray image gridding method based on image projection transformation and power spectral analysis is discussed in Feng et al. (2015) .  ... 
doi:10.1016/j.jesit.2016.06.001 fatcat:2p2uyvaflzbdhjyuffew2pjyti

Theoretical Framework for Spatial Resolution in Edge-Illumination X-Ray Tomography

Charlotte K. Hagen, Fabio A. Vittoria, Marco Endrizzi, Alessandro Olivo
2018 Physical Review Applied  
In this article, we provide a theoretical framework for the spatial resolution of this method, based on the concept of the bowtie-shaped essential support of the Radon transform in frequency space, which  ...  and the sample thickness.  ...  that the spectral content of the Radon transform is confined to a well-defined area that has the shape of a bowtie.  ... 
doi:10.1103/physrevapplied.10.054050 fatcat:kc4r5edqcbfsxlkq2zrf7vq3mi

Principled Design and Implementation of Steerable Detectors [article]

Julien Fageot, Virginie Uhlmann, Zsuzsanna Püspöki, Benjamin Beck, Michael Unser, Adrien Depeursinge
2021 arXiv   pre-print
We provide a complete pipeline for the detection of patterns of interest in an image.  ...  We show that the detection performance drastically improves when we exploit the statistics of the background via its power-spectrum decay, which we refer to as spectral-shaping.  ...  ACKNOWLEDGEMENTS The authors would like to thank Emrah Bostan for his precious help regarding the statistical estimation of self-similarity parameters.  ... 
arXiv:1811.00863v2 fatcat:j23jdyfzavftbgbg5ppc2pwzpe

Page 3509 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
However, so far, this generalized analysis did not allow for an appropriate spectral analysis of nonstationary processes, in particular 1/f noise (f represents frequency).  ...  This property is, among others, useful in the image segmentation domain, which we address specifically. Further, we propose a cellular coevolutionary algorithm for the optimization of the model.  ... 

Enhancing and replacing spectral information with intermediate structural inputs: A case study on impervious surface detection

Giorgos Mountrakis, Li Luo
2011 Remote Sensing of Environment  
This partial classification acted as the basis for the production of linear features using an iterative Radon transform.  ...  This finding offers an important contribution to the remote sensing community, since the proposed methodology handles the missing spectral information problem through exclusive analysis of the given degraded  ...  the Syracuse Center of Excellence CARTI Program.  ... 
doi:10.1016/j.rse.2010.12.018 fatcat:wld3htzehvf2hpgy75wu2cmugy

Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem

Leonid P. Yaroslavsky, Gil Shabat, Benjamin G. Salomon, Ianir A. Ideses, Barak Fishbain
2009 Optical Society of America. Journal A: Optics, Image Science, and Vision  
Conditions for the image unique recovery, from sparse samples, are formulated and then analyzed for various transforms.  ...  In this paper, we address this problem in a framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of non-zero transform coefficients in a certain transform  ...  Averbuch, School of Computer Science, Tel-Aviv University, Israel, for his help with respect to the discrete stable forward and inverse Radon transforms.  ... 
doi:10.1364/josaa.26.000566 pmid:19252655 fatcat:e6pbb7aiv5cjnafppbyvovcf3i

Sliced and Radon Wasserstein Barycenters of Measures

Nicolas Bonneel, Julien Rabin, Gabriel Peyré, Hanspeter Pfister
2014 Journal of Mathematical Imaging and Vision  
The first method makes use of the Radon transform of the measures, and the second is the solution of a convex optimization problem over the space of measures.  ...  We show numerical approximation schemes based on a discrete Radon transform and on the resolution of a non-convex optimization problem.  ...  Jones for useful feedback on our draft. We also thank the authors of all the images used to demonstrate our color transfers. This work has been partially supported by NSF CGV-1111415.  ... 
doi:10.1007/s10851-014-0506-3 fatcat:wehqpntdtfdarhoiyhgtjwrodi

Efficient Non-Line-of-Sight Imaging from Transient Sinograms [article]

Mariko Isogawa, Dorian Chan, Ye Yuan, Kris Kitani, Matthew O'Toole
2020 arXiv   pre-print
transform these sinusoidal measurements into 3D positions of hidden scatterers or NLOS images of hidden objects, and (3) despite operating on an order of magnitude fewer measurements than previous approaches  ...  One approach involves using pulsed lasers and ultrafast sensors to measure the travel time of multiply scattered light.  ...  We thank Ioannis Gkioulekas for helpful discussions and feedback on this work. M. Isogawa is supported by NTT Corporation. M. O'Toole is supported by the DARPA REVEAL program.  ... 
arXiv:2008.02787v1 fatcat:zvzvx3nttbchjafejvyj2mfq3i

Time-Frequency Bibliography [chapter]

2003 Time Frequency Analysis  
, 260 -design of, 76 -design of kernels for, 170-173 -discrete kernels for, 173-175 -in Doppler-lag domain, 169-170 -of dolphin click, 176 -of electric power disturbances, 628-631, 634 -optimization  ...  form, 238 -general quadratic, 235-238 -IF property for, 239 -properties related to kernel, 239-241 -real-time computation of, 269-270 -sampling for, 236-238 -with Doppler-independent kernels,  ... 
doi:10.1016/b978-008044335-5/50038-3 fatcat:tfc7wkllejcdvcbtqalinh5t3y

A box spline calculus for computed tomography

Alireza Entezari, Michael Unser
2010 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms.  ...  In particular, we prove that the 2-D Radon transform of an Ndirection box spline is generally a (non-uniform) polynomial spline of degree N − 1.  ...  for P θ {ϕ}(y), the X-ray (or Radon) transform of the B-spline generator.  ... 
doi:10.1109/isbi.2010.5490105 dblp:conf/isbi/EntezariU10 fatcat:67stwgonvfejnnwdgpzn3dnob4

Tomographic Feature-Based Map Merging for Multi-Robot Systems

Lee
2020 Electronics  
The first part of the proposed method is to estimate a map transformation matrix using the Radon transform which can extract tomographically salient features from individual grid maps.  ...  This paper addresses the problem of grid map merging to obtain the collective map information in multi-robot systems with unknown initial poses.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/electronics9010107 fatcat:4dgrsrtzjrecnosjyvtrbnh7ta
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