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A geometric projection-space reconstruction algorithm

Jerry L. Prince, Alan S. Willsky
1990 Linear Algebra and its Applications  
We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles.  ...  , and periodicity of the 2-D Radon transform.  ...  If, for example, a noisy measurement of a true Radon transform has any two projections that do not integrate to the same value, then the measurement is not a valid Radon transform, and it follows that  ... 
doi:10.1016/0024-3795(90)90211-t fatcat:iefvticmnnfofdp5uqtyqay4we

From Particle Mechanics to Pixel Dynamics: Utilizing Stochastic Resonance Principle for Biomedical Image Enhancement [chapter]

V.P.Subramanyam Rallabandi, Prasun Kumar
2011 Thermodynamics - Systems in Equilibrium and Non-Equilibrium  
be formed using respective Fourier integral transform (eq. 6a) and Radon transform (eq. 6b) which is given by (Rallabandi & Roy, 2008) : where δ(.) is a dirac-delta function given for the plane of projection  ...  (a) Noisy or hazy CT image (b) SR-enhanced output image using Radon transform Fig. 6 . 6 (a) Noisy MR image (b) SR-enhanced image where the lesion, sulci and gyri are visible (c) & (d) Image histograms  ...  From Particle Mechanics to Pixel Dynamics: Utilizing Stochastic Resonance Principle for Biomedical Image Enhancement, Thermodynamics -Systems in Equilibrium and Non-Equilibrium, Dr.  ... 
doi:10.5772/25154 fatcat:zr6jjxgmprepfdnvm5npmwznjq

Stochastic Deconvolution Over Groups

B. Yazici
2004 IEEE Transactions on Information Theory  
This is a rich area of research with applications to Radon transform inversion for tomography, wide-band and narrow-band signal processing, inverse rendering in computer graphics, and channel estimation  ...  Key components of our approach are group representation theory and the concept of group stationarity.  ...  Radon Transform Inversion for Tomographic Image Reconstruction The Radon transform and its generalizations arise in diverse engineering applications, including medical imaging, synthetic-aperture radar  ... 
doi:10.1109/tit.2004.824916 fatcat:g3l2zm4kmzhmbaq27a7tlykpia

An empirical study of algebraic-reconstruction techniques [chapter]

Ehsan Kazemi, Nedialko Nedialkov
2013 Computational Vision and Medical Image Processing IV  
The problem of reconstructing images from measurements of X-ray radiation belongs to the class of inverse prob- lems.  ...  the reconstructed image.  ...  Central Slice Theorem This theory was first derived by Bracewell in 1956 [3] and involves the interaction between the Radon transform and the Fourier transform, which is known as either central projection  ... 
doi:10.1201/b15810-19 fatcat:pfwnslhdzzfdro6kjeynpz5rre

Flaw reconstruction in NDE using a limited number of X-ray radiographic projections

1992 NDT & E international  
The author also thanks Dave Utrata of the AAR for arranging the test frog radiography and for his continuous interest in this work.  ...  ACKNOWLEDGEMENTS The author would like to thank the following people for their assistance during this research: John Basart, Joe Gray, Don Thompson, Hsien-Sen Hung, Noel Cressie, Steve Russell, T.V.  ...  The NDE field uses a wide range of theories from different areas such as electromagnetics, physics and fracture mechanics.  ... 
doi:10.1016/0963-8695(92)90261-e fatcat:qb26rd7odvcfpjnrpm6iw6f7pq

Dynamic masking of PIV images using the Radon transform in free surface flows

Arnaud Sanchis, Atle Jensen
2011 Experiments in Fluids  
The Radon transform-based technique presented in this paper allows the automatic detection of the air-water interface in a stream of particle images acquired from a single camera.  ...  Accuracy estimations are provided using synthetic and real wave profiles. An extension to the more complex case of an overturning wave is also discussed.  ...  The authors are also grateful to Charlotte Sanchis from Fugro-Geoteam for helpful discussions.  ... 
doi:10.1007/s00348-011-1101-7 fatcat:urxp32rw2vbdvpisgdc5agpnx4

Applications of laser speckle photography for thermal flow problems

K.D. Kihm
1998 Optics and lasers in engineering  
modified to apply for the laser speckle tomography. ¹he reconstruction accuracy of AR¹ is compared with Fourier convolution (FC) technique particularly under a limited number of projections.  ...  Finally, tomographic reconstruction of laser speckle photography data is discussed using density computer-synthesized phantom fields. ¹he conventional algebraic reconstruction technique (AR¹) has been  ...  This section discusses the axisymmetric test fields, which can be readily reconstructed by a mathematical inversion from a single projection, called Radon transformation.  ... 
doi:10.1016/s0143-8166(97)00084-5 fatcat:x7l5jbjwsjefllijxlcybghgmi

Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomography [article]

Simon Maretzke
2015 arXiv   pre-print
by the Fourier transform.  ...  We consider both the near-field- or Fresnel regime characterized by a moderate propagation length between sample and detector and the far-field limit of large detector distances, where propagation is governed  ...  Based on the mathematical theory of the Radon transform and its inversion [90] laid down almost a hundred years ago, three-dimensional images are reconstructed from these measurements.  ... 
arXiv:1502.05073v1 fatcat:cgstp3dpxffudhahtob37ghxcy

10 Maximum-Likelihood Estimationin Experimental Quantum Physics [chapter]

Gerald Badurek, Zdeněk Hradil, Alexander Lvovsky, Gabriel Molina-Teriza, Helmut Rauch, Jaroslav Řeháček, Alipasha Vaziri, Michael Zawisky
2004 Lecture Notes in Physics  
The theory of quantum state reconstruction is illustrated here on several examples taken from modern experimental praxis.  ...  All these experiments nicely demonstrate the utility of present state-of-art techniques for manipulating states of a neutron and internal as well as external states of a photon.  ...  Acknowledgments The authors would like to acknowledge support by the following grants and projects. J.Řeháček and Z. Hradil: Grant No. LN00A015 of the Czech Min-  ... 
doi:10.1007/978-3-540-44481-7_10 fatcat:jw4jlzv7sbe6bnracg6wv73e7q

A local update strategy for iterative reconstruction from projections

K. Sauer, C. Bouman
1993 IEEE Transactions on Signal Processing  
1 Iterative methods for statistically-based reconstruction from projections are computationally costly relative to convolution backprojection, but allow useful image reconstruction from sparse and noisy  ...  This paper includes analysis of the convergence properties of gradient ascent and GS for reconstruction from integral projections, and simulations of both maximum-likelihood and maximum a posteriori cases  ...  of a Gauss-Seidel algorithm for the iterative image reconstruction from projections using Bayesian criteria.  ... 
doi:10.1109/78.193196 fatcat:zw7rp4i37vclli3aabei3pyc2e

CNN-based regularisation for CT image reconstructions [article]

Attila Juhos
2022 arXiv   pre-print
Physical measurements are post-processed by mathematical reconstruction algorithms that may offer weaker or top-notch consistency guarantees on the computed volumetric field.  ...  In this report algorithms are presented that take as input a slice of a low-quality reconstruction of the volume in question and aim to map it to the reconstruction that is considered ideal, the ground  ...  Here I would like to thank my supervisor, Dániel Hadházi for his patience and everlasting support in our work.  ... 
arXiv:2201.09132v1 fatcat:6ql63dounbcuhcdsr4haq5aecy

Cramer-Rao bounds for parametric shape estimation in inverse problems

Jong Chul Ye, Y. Bresler, P. Moulin
2003 IEEE Transactions on Image Processing  
The bounds reveal that highly accurate parametric reconstructions are possible in these examples, using severely limited and noisy data.  ...  As an illustration, we derive explicit formulas for computed tomography, Fourier imaging, and deconvolution problems.  ...  Computed Tomography Consider tomographic reconstruction from line-integral projections or the samples of the 2-D Radon transform.  ... 
doi:10.1109/tip.2002.806249 pmid:18237880 fatcat:jdqnj7n7l5hgdesmmyrzgtahcm

An Alternative Model to Radon Transform for Gamma Ray Emission Tomography

Christian Jeanguillaume, Richard Simonnet, Christine Cavaro-Menard, Abdelha Douiri, Ines Bouali, Jean Jacques Loeb
2017 Advances in Molecular Imaging  
The Radon transform fits badly Single Photon Emission Tomography (SPECT). However, Thin Holes Collimator (THC) and Radon model are widely used.  ...  of the reconstructed images?  ...  Advances in Molecular Imaging Aknowledgements This study was supported by the "Pays de Loire" MPIA Grant.  ... 
doi:10.4236/ami.2017.72002 fatcat:ukbibawutbe2rbs5tt245qspru

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

Ashkan Javaherian, Manuchehr Soleimani, Knut Moeller
2014 Physiological Measurement  
., 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum.  ...  Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously done  ...  Acknowledgements This work was partially supported by the Federal Ministry of Education and Research (BMBF) in Germany under grant no. 03FH038I3 (MOSES).  ... 
doi:10.1088/0967-3334/36/1/43 pmid:25501046 fatcat:hodumwjcfzhufnfxuttxurygya

RODEO: Robust DE-aliasing autoencOder for Real-time Medical Image Reconstruction [article]

Janki Mehta, Angshul Majumdar
2019 arXiv   pre-print
In this work we address the problem of real-time dynamic medical MRI and X Ray CT image reconstruction from parsimonious samples Fourier frequency space for MRI and sinogram tomographic projections for  ...  In fact, it is fast enough for real-time reconstruction the images are reconstructed as fast as they are acquired with only slight degradation of image quality.  ...  Other analytic techniques have evolved for CT reconstruction (from radon transform) [67, 68], but for our problem the fast and simple FBP suffices.  ... 
arXiv:1912.07519v1 fatcat:2nndsu6snbe4hoollz4v3yqe4i
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