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An algorithm for the reconstruction of discrete sets from two projections in presence of absorption

Elena Barcucci, Andrea Frosini, Simone Rinaldi
2005 Discrete Applied Mathematics  
In this paper we consider the problem of reconstructing a binary matrix from absorbed projections, as introduced in [Kuba and Nivat, Linear Algebra Appl. 339 (2001) 171-194].  ...  In particular we prove that two left and right horizontal absorbed projections along a single direction uniquely determine a row of a binary matrix for a specific absorption coefficient.  ...  Acknowledgements The authors wish to thank the referees whose helpful suggestions greatly improved the final version of the paper.  ... 
doi:10.1016/j.dam.2005.02.020 fatcat:cfenihz5pjfdda7hh7mwxwqs7i

The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences [article]

Yuxin Chen, Emmanuel Candes
2017 arXiv   pre-print
We expect this algorithmic framework to be effective for a broad range of discrete assignment problems.  ...  Starting with a first guess computed via a spectral method, the algorithm successively refines the iterates via projected power iterations.  ...  C. is partially supported by NSF via grant DMS-1546206, and by the Math + X Award from the Simons Foundation. Y. C. is supported by the same award.  ... 
arXiv:1609.05820v3 fatcat:se3bc676wzflrfzhoggxzn7bv4

An iterative maximum-likelihood polychromatic algorithm for CT

B. De Man, J. Nuyts, P. Dupont, G. Marchal, P. Suetens
2001 IEEE Transactions on Medical Imaging  
The algorithm prevents beam hardening artifacts by incorporating a polychromatic acquisition model. The continuous spectrum of the X-ray tube is modeled as a number of discrete energies.  ...  A new iterative maximum-likelihood reconstruction algorithm for X-ray computed tomography is presented.  ...  ACKNOWLEDGMENT The authors would like to thank the people from Siemens Medical Systems (S. Schaller in particular) for their cooperation.  ... 
doi:10.1109/42.959297 pmid:11686446 fatcat:na3b3jt66zb7pcv5nabvajaniy

Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

Leonid A Kunyansky
2008 Inverse Problems  
After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform  ...  We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case).  ...  In order to compare stability of our algorithm to that of the classical FBP, we have reconstructed the two phantoms (shown in figures 2(a) and 4(a)) using the latter method, from a similar number of the  ... 
doi:10.1088/0266-5611/24/5/055021 fatcat:qnq6jbxkdbegddg22j7sg3f7wu

An EM algorithm for dynamic SPECT

H.H. Bauschke, D. Noll, A. Celler, J.M. Borwein
1999 IEEE Transactions on Medical Imaging  
In this paper we present two variants of the EM algorithm for dynamic SPECT imaging.  ...  Some preliminary numerical tests indicating the feasibility of the method are included.  ...  Fig. 3 . 3 Comparisons of models (2) and (4) using typical dynamic pixels from two simulated reconstructions on the basis of 60 (left column) and 80 (right column) camera positions.  ... 
doi:10.1109/42.764899 pmid:10363703 fatcat:mhbmyya5lvaoza5aaf4wkvzama

Computational design of acoustic materials using an adaptive optimization algorithm [article]

Larisa Beilina, Eugene Smolkin
2017 arXiv   pre-print
Efficiency of the presented adaptive optimization algorithm is illustrated on the construction of the symmetric acoustic material in two dimensions.  ...  We consider the problem of the construction of the acoustic structure of arbitrary geometry with prescribed desired properties.  ...  The research of E.S. is supported by the Ministry of Education and Science of the Russian Federation, Project No. 1.894.2017/Π.  ... 
arXiv:1701.06006v3 fatcat:jt4eviiypvauvgq2cczdqc7nhm

The design and implementation of COSEN, an iterative algorithm for fully 3-D listmode data

R. Levkovilz, D. Falikman, M. Zibulevsky, A. Ben-Tal, A. Nemirovski
2001 IEEE Transactions on Medical Imaging  
In this paper,we present coincidence-list-ordered sets expectation-maximization (COSEM), an algorithm for iterative image reconstruction directly from list-mode coincidence acquisition data.  ...  We present an adaptation of COSEM to the Varicam VG camera and show results from clinical and phantom studies.  ...  The OSEM and the EM algorithms use binned data (e.g., projection sets) to reconstruct the image.  ... 
doi:10.1109/42.932747 pmid:11465469 fatcat:uksj63byubhpfouz27kqebnohu

An Algorithm for Pattern Discovery in Time Series [article]

Cosma Rohilla Shalizi, Kristina Lisa Shalizi, James P. Crutchfield
2002 arXiv   pre-print
We also illustrate its behavior on an example process, and report selected numerical results from an implementation.  ...  We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal  ...  Acknowledgments Our work has been supported by the Dynamics of Learning project at SFI, under DARPA cooperative agreement F30602-00-2-0583, and by the Network Dynamics Program here, which is supported  ... 
arXiv:cs/0210025v3 fatcat:tkkj4vuvpfhnvix67emgs2ukfi

An Adaptive Base Point Algorithm for the Retrieval of Aerosol Microphysical Properties

L. Osterloh
2011 The Open Atmospheric Science Journal  
We consider the basic equation as an ill-posed problem and solve the system derived from spline collocation via a Padé iteration.  ...  The algorithm takes special care of the fact that the reconstruction of the distribution via spline collocation is very sensitive to the choice of base points of the chosen spline basis.  ...  That means that a set of 100 different sets of perturbed data were processed by each algorithm.  ... 
doi:10.2174/1874282301105010061 fatcat:duxlphlqkzcbzpypw3mqvvqgri

Properties of the Center of Gravity as an Algorithm for Position Measurements: Two-Dimensional Geometry [article]

Gregorio Landi
2021 arXiv   pre-print
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry.  ...  Simulations, adapted to the CMS em-calorimeter and to a triangular detector array, are provided for energy and position reconstruction algorithms with a finite number of detectors.  ...  This discretization is the principal source of systematic error of the COG as a position reconstruction algorithm.  ... 
arXiv:2103.03449v1 fatcat:zhdsf6gavjaphgxrtikarzvrtu

Real-time photoacoustic projection imaging using deep learning [article]

Johannes Schwab, Stephan Antholzer, Robert Nuster, Markus Haltmeier
2018 arXiv   pre-print
The proposed network is shown to outperform state-of-the-art iterative total variation reconstruction algorithms in terms of reconstruction speed as well as in terms of various evaluation metrics.  ...  Photoacoustic tomography (PAT) is an emerging and non-invasive hybrid imaging modality for visualizing light absorbing structures in biological tissue.  ...  Acknowledgement SA and MH acknowledge support of the Austrian Science Fund (FWF), project P 30747-N32. The work of RN has been supported by the FWF, project P 28032.  ... 
arXiv:1801.06693v4 fatcat:h7lz7366hjdpthka4bqnhjgysy

Adaptive filtered-back-projection for computed tomography

Joseph Shtok, Michael Elad, Michael Zibulevsky
2008 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel  
We propose an extension of the Filtered Back-Projection (FBP) algorithm for reconstruction of attenuation images in Computed Tomography (CT).  ...  The resulting adaptive scheme absorbs various imperfections of reconstruction algorithm and specializes to given task, effectively improving the reconstruction quality.  ...  SUMMARY We have presented an extension of the basic direct algorithm for CT reconstruction -the Filtered Back-projection (FBP).  ... 
doi:10.1109/eeei.2008.4736585 fatcat:hwbnpb3mrfburpsnps4ewrqjl4

Multiple projection optical diffusion tomography with plane wave illumination

Vadim A Markel, John C Schotland
2005 Physics in Medicine and Biology  
Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs.  ...  The advantage of the proposed method is that the measured data can be much more easily fitted into the dynamic range of most commonly used detectors.  ...  The resulting reconstruction formula is no longer an SVD pseudo-inverse on the whole set of data ψ(ω, ρ d , θ).  ... 
doi:10.1088/0031-9155/50/10/012 pmid:15876672 fatcat:t2mt427cpjagzprlroikkmrqbm

Dual-projection optical diffusion tomography

Vadim A. Markel, John C. Schotland
2004 Optics Letters  
The second projection improves image quality due to the fact that the depth and transverse directions are interchanged. An image reconstruction algorithm is derived and illustrated with simulations.  ...  It is shown that the spatial resolution of images improves by a factor of 4 -5 due to the second projection.  ...  We now turn to the derivation of an image reconstruction algorithm that utilizes simultaneously the data obtained from two orthogonal projections shown in Fig. 1 .  ... 
doi:10.1364/ol.29.002019 pmid:15455766 fatcat:xnj7fakonfhy5htsravtts6evm

Reconstruction of hv-convex binary matrices from their absorbed projections

Attila Kuba, Antal Nagy, Emese Balogh
2004 Discrete Applied Mathematics  
The reconstruction of hv-convex binary matrices from their absorbed projections is considered.  ...  Also a reconstruction algorithm is given to determine the whole structure of hv-convex binary matrices from such projections. ?  ...  Introduction The reconstruction of binary matrices from their row and column sums is a basic problem in discrete tomography (DT).  ... 
doi:10.1016/j.dam.2002.11.001 fatcat:n4gir2loxrh3jibsjn4xfgb7le
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