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Weighted sampling and reconstruction in weighted reproducing kernel spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2010年第1期367卷 34-42页

作者： Xian, Jun Sun Yat Sen Zhongshan Univ Dept Math Guangzhou 510275 Guangdong Peoples R China

In this paper, we discuss sampling and reconstruction of signals in the weighted reproducing kernel space associated with an idempotent integral operator. We show that any signal in that space can be stably reconstructed from its weighted samples taken on a relatively-separated set with sufficiently small gap. We also develop an iterative reconstruction algorithm for the reconstruction of a signal from its weighted samples taken on a relatively-separated set with sufficiently small gap. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Sampling reconstruction algorithm Reproducing kernel space Idempotent operator Weight

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A reconstruction Method for Electrical Impedance Tomography Using Particle Swarm Optimization

A Reconstruction Method for Electrical Impedance Tomography ...

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International Conference on Life System Modeling and Simulation / International Conference on Intelligent Computing for Sustainable Energy and Environment (LSMS-ICSEE)

作者： Chen, Min-you Hu, Gang He, Wei Yang, Yan-li Zhai, Jin-qian Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Se Chongqing 400044 Peoples R China

ISBN: (纸本)9783642155963

The inverse problem of Electrical Impedance Tomography (EIT), especially for open EIT which involves less measurement, is a non-linear ill-posed problem. In this paper, a novel method based on Particle Swarm Optimization (PSO) is proposed to solve the open EIT inverse problem. This method combines a modified Newton-Raphson algorithm, a conductivity-based clustering algorithm, with an adaptive PSO algorithm to enhance optimal search capability and improve the quality of the reconstructed image. The results of numerical simulations show that the proposed method has a faster convergence to optimal solution and higher spatial resolution on a reconstructed image than a Newton-Raphson type algorithm.

关键词： Open Electrical Impedance Tomography reconstruction algorithm Clustering Particle Swarm Optimization

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reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution

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OPTICS LETTERS 2006年第11期31卷 1633-1635页

作者： Zhang, FC Pedrini, G Osten, W Univ Stuttgart Inst Tech Opt D-70569 Stuttgart Germany

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system's transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented. (c) 2006 Optical Society of America.

关键词： Coordinate system Holograms resolution limit Planing diffraction reconstruction algorithm Resolving power

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Compact polarimetric SAR interferometry

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IET RADAR SONAR AND NAVIGATION 2010年第3期4卷 449-456页

作者： Lavalle, M. Solimini, D. Pottier, E. Desnos, Y. -L. Univ Roma Tor Vergata DISP I-00133 Rome Italy Univ Rennes 1 CNRS UMR 6164 IETR F-35042 Rennes France ESA ESRIN I-00144 Frascati Italy

The authors discuss the role and performance of compact polarimetry in SAR interferometry. The considered SAR architecture transmits either a linearly polarised wave oriented at 45 degrees or a circularly polarised one, and receives at horizontal and vertical polarisation. Two polarimetric acquisitions are combined in an interferometric image, characterised by a polarimetric and interferometric (POLINSAR) covariance matrix. The expression of the covariance matrix for compact polarimetry is derived and the relationship between compact and full polarimetric covariance matrices is discussed. On the basis of symmetry properties of geophysical media, the authors propose a reconstruction algorithm of the full polarimetric information from a compact polarimetric dataset. The algorithm allows the assessment of compact POLINSAR and the comparison between the two compact configurations. The authors consider forested areas and compare the interferometric degree of coherence measured at different polarisations by compact polarimetry and full polarimetry. The study shows that the degree of coherence from a compact polarimetric architecture carries enough information for POLINSAR applications, such as forest parameters retrieval, if the symmetry properties are satisfied. Airborne data acquired by the DLR E-SAR sensor over the Traunstein forest are used to illustrate the results.

关键词： reconstruction algorithm polarimetry Covariance matrix coherence Polarization variance covariance matrix

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ASYMPTOTIC IMAGING OF PERFECTLY CONDUCTING CRACKS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2010年第2期32卷 894-922页

作者： Ammari, Habib Kang, Hyeonbae Lee, Hyundae Park, Won-Kwang ESPCI CNRS UMR 7587 Inst Langevin F-75231 Paris 05 France Inha Univ Dept Math Inchon 402751 South Korea Kookmin Univ Dept Math Seoul 136702 South Korea

In this paper, we consider cracks with Dirichlet boundary conditions. We first derive an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack. Based on this formula, we design a noniterative approach for locating a collection of small cracks. In order to do so, we construct a response matrix from the boundary measurements. The location and the length of the crack are estimated, respectively, from the projection onto the noise space and the first significant singular value of the response matrix. Indeed, the direction of the crack is estimated from the second singular vector. We then consider an extended crack with Dirichlet boundary conditions. We rigorously derive an asymptotic expansion for the boundary perturbations that are due to a shape deformation of the crack. To reconstruct an extended crack from many boundary measurements, we develop two methods for obtaining a good guess. Several numerical experiments show how the proposed techniques for imaging small cracks as well as those for obtaining good initial guesses toward reconstructing an extended crack behave.

关键词： crack detection asymptotic imaging reconstruction algorithm

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Towards automated electron holographic tomography for 3D mapping of electrostatic potentials

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ULTRAMICROSCOPY 2010年第5期110卷 390-399页

作者： Wolf, Daniel Lubk, Axel Lichte, Hannes Friedrich, Heiner Tech Univ Dresden Inst Struct Phys Triebenberg Lab D-01062 Dresden Germany Univ Utrecht Debye Inst Nanomat Sci NL-3584 CA Utrecht Netherlands

Electron-holographic tomography (EHT), that is, the combination of off-axis electron holography with electron tomography, was successfully applied for the quantitative 3D mapping of electrostatic potentials at the nanoscale. Here we present the first software package (THOMAS) for semi-automated acquisition of holographic tilt series, a prerequisite for efficient data collection. Using THOMAS, the acquisition time for a holographic tilt series, consisting of object and reference holograms, is reduced by a factor of five on average, compared to the previous, completely manual approaches. Moreover, the existing software packages for retrieving amplitude and phase information from electron holograms have been extended, now including a one-step procedure for holographic tilt series reconstruction. Furthermore, a modified SIRT algorithm (WSIRT) was implemented for the quantitative 3D reconstruction of the electrostatic potential from the aligned phase tilt series. Finally, the application of EHT to a polystyrene latex sphere test-specimen and a pn-doped Ge 'needle'-shaped specimen are presented, illustrating the quantitative character of EHT. For both specimens the mean inner potential (MIP) values were accurately determined from the reconstructed 3D potential. For the Ge specimen, additionally the 'built-in' voltage across the pn junction of 0.5 V was obtained. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Electron holography Electron tomography Automation Acquisition software reconstruction algorithm Electrostatic potential

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The imaging performance of a LaBr₃-based PET scanner

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PHYSICS IN MEDICINE AND BIOLOGY 2010年第1期55卷 45-64页

作者： Daube-Witherspoon, M. E. Surti, S. Perkins, A. Kyba, C. C. M. Wiener, R. Werner, M. E. Kulp, R. Karp, J. S. Univ Penn Dept Radiol Philadelphia PA 19104 USA

A prototype time-of-flight (TOF) PET scanner based on cerium-doped lanthanum bromide [LaBr3 (5% Ce)] has been developed. LaBr3 has a high light output, excellent energy resolution and fast timing properties that have been predicted to lead to good image quality. Intrinsic performance measurements of spatial resolution, sensitivity and scatter fraction demonstrate good conventional PET performance;the results agree with previous simulation studies. Phantom measurements show the excellent image quality achievable with the prototype system. Phantom measurements and corresponding simulations show a faster and more uniform convergence rate, as well as more uniform quantification, for TOF reconstruction of the data, which have 375 ps intrinsic timing resolution, compared to non-TOF images. Measurements and simulations of a hot and cold sphere phantom show that the 7% energy resolution helps to mitigate residual errors in the scatter estimate because a high energy threshold (>480 keV) can be used to restrict the amount of scatter accepted without a loss of true events. Preliminary results with incorporation of a model of detector blurring in the iterative reconstruction algorithm not only show improved contrast recovery but also point out the importance of an accurate resolution model of the tails of LaBr3's point spread function. The LaBr3 TOF-PET scanner demonstrated the impact of superior timing and energy resolutions on image quality.

关键词： reconstruction algorithm Scattering FEZF2 gene Energy resolution Optical output Positron Emission Tomography Systems Image quality Tail Imaging Phantom

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Mathematical Modeling in Photoacoustic Imaging of Small Absorbers

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SIAM REVIEW 2010年第4期52卷 677-695页

作者： Ammari, Habib Bossy, Emmanuel Jugnon, Vincent Kang, Hyeonbae Ecole Normale Super Dept Math & Applicat F-75005 Paris France ESPCI ParisTech CNRS Inst Langevin UMR 7587 F-75231 Paris France Ecole Polytech CNRS Ctr Math Appl UMR 7641 F-91128 Palaiseau France Inha Univ Dept Math Inchon 402751 South Korea

This paper is devoted to mathematical modeling in photoacoustic imaging of small absorbers. We propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal. We also show the focusing property of the back-propagated acoustic signal. Indeed, we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal. The first method consists of a MUltiple SIgnal Classification (MUSIC)-type algorithm and the second one uses a multifrequency approach. We also show results of computational experiments to demonstrate efficiency of the algorithms.

关键词： photoacoustic imaging small absorbers wave equation asymptotic expansion reconstruction algorithm MUSIC algorithm multifrequency imaging approach optical tomography

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Differential Evolution Approach for Regularized Bioluminescence Tomography

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2010年第9期57卷 2229-2238页

作者： Cong, Alexander Cong, Wenxiang Lu, Yujie Santago, Peter Chatziioannou, Arion Wang, Ge Virginia Polytech Inst & State Univ ICTAS Ctr Biomed Imaging WFU VTSch Biomed Eng & Sci Blacksburg VA 24061 USA Virginia Polytech Inst & State Univ Biomed Imaging Div WFU VTSch Biomed Eng & Sci Blacksburg VA 24061 USA Univ Texas Hlth Sci Ctr Houston Inst Mol Med Ctr Mol Imaging Houston TX 77030 USA Virginia Polytech Inst & State Univ Dept Elect & Comp Engn Blacksburg VA 24060 USA Wake Forest Univ Sch Med Dept Biomed Engn Winston Salem NC 27157 USA Univ Calif Los Angeles David Geffen Sch Med Dept Med & Mol Pharmacol Los Angeles CA 90095 USA

Bioluminescence tomography (BLT) is an inverse source problem that localizes and quantifies bioluminescent probe distribution in 3-D. The generic BLT model is ill-posed, leading to nonunique solutions and aberrant reconstruction in the presence of measurement noise and optical parameter mismatches. In this paper, we introduce the knowledge of the number of bioluminescence sources to stabilize the BLT problem. Based on this regularized BLT model, we develop a differential evolution-based reconstruction algorithm to determine the source locations and strengths accurately and reliably. Then, we evaluate this novel approach in numerical, phantom, and mouse studies.

关键词： Bioluminescence tomography (BLT) differential evolution (DE) diffusion approximation (DA) inverse source problem reconstruction algorithm

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Stereoscopic 3D Sports Content Without Stereo Rigs

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SMPTE MOTION IMAGING JOURNAL 2010年第7期119卷 51-55页

作者： Grau, Oliver Vinayagamoorthy, Vinoba UCL London WC1E 6BT England

This contribution describes an alternative approach to generating stereoscopic content of sports scenes from regular broadcast cameras without the need for special stereo rigs. This is achieved by using 3D reconstruction previously developed for applications in postmatch analysis. The reconstruction method requires at least four or five cameras and computes the 3D information automatically. Two different target formats for the delivery of stereoscopic 3D TV are discussed: the display-independent layered depth video format and conventional binocular stereo. The results viewed on two different displays demonstrate the potential of the method as an alternative production method for stereoscopic 3D content.

关键词： reconstruction algorithm Stereoscopic Drilling rigs Sports Stereo image processing production methods three-dimensional television Cameras three-dimensional displays Obstetric Delivery

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