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Random Average Sampling in a Reproducing Kernel Subspace of Mixed Lebesgue Space L^p,q(Rⁿ⁺¹)

RESULTS IN MATHEMATICS 2024年第1期79卷 9-9页

作者： Patel, Dhiraj Sivananthan, S. Indian Inst Technol Delhi Dept Math New Delhi 110016 India

In this paper, we study average sampling inequality in a probabilistic framework for a reproducing kernel subspace V of mixed Lebesgue space. More precisely, we show with high probability that a function concentrated on a compact cube C can be stably recovered from their O(mu (C) log mu (C)) many average values at uniformly distributed random points over C, where mu is a Lebesgue measure. Further, we propose an exponential convergence reconstruction scheme to reconstruct the concentrated function from their random average measurements and illustrate with an example.

关键词： Reproducing kernel space mixed Lebesgue space random sampling reconstruction algorithm Idempotent operator Average sampling inequality

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Inverse problems on low-dimensional manifolds

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NONLINEARITY 2023年第1期36卷 734-808页

作者： Alberti, Giovanni S. Arroyo, Angel Santacesaria, Matteo Univ Genoa MaLGa Ctr Dept Math Via Dodecaneso 35 I-16146 Genoa Italy Univ Complutense Madrid Interdisciplinary Math Inst MOMAT Res Grp Dept Appl Math & Math Anal Madrid 28040 Spain

We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we assume that the unknown belongs to a finite-dimensional manifold: this assumption arises in many real-world scenarios where natural objects have a low intrinsic dimension and belong to a certain submanifold of a much larger ambient space. We prove uniqueness and Holder and Lipschitz stability results in this general setting, also in the case when only a finite discretization of the measurements is available. Then, a Landweber-type reconstruction algorithm from a finite number of measurements is proposed, for which we prove global convergence, thanks to a new criterion for finding a suitable initial *** general results are then applied to several examples, including two classical nonlinear ill-posed inverse boundary value problems. The first is Calderon's inverse conductivity problem, for which we prove a Lipschitz stability estimate from a finite number of measurements for piece-wise constant conductivities with discontinuities on an unknown triangle. A similar stability result is then obtained for Gel'fand-Calderon's problem for the Schrodinger equation, in the case of piece-wise constant potentials with discontinuities on a finite number of non-intersecting balls.

关键词： inverse problems Calderon problem Gel'fand-Calderon problem machine learning manifolds Lipschitz stability reconstruction algorithm

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Optimization of the Acquisition Time and Injected Dose of ¹⁸ F-Fluorodeoxyglucose Based on Patient Specifications for High-Sensitive Positron Emission Tomography/Computed Tomography Scanner

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WORLD JOURNAL OF NUCLEAR MEDICINE 2023年第3期22卷 196-202页

作者： Al-Fatlawi, Murtadha Pak, Farideh Farzanefar, Saeed Salehi, Yalda Monsef, Abbas Sheikhzadeh, Peyman AL Mustaqbal Univ Coll Radiol Tech Dept Babel Iraq Washington Univ Dept Radiol Oncol St Louis MO USA Univ Tehran Med Sci Imam Khomeini Hosp Complex Dept Nucl Med Tehran Iran Univ Minnesota Ctr Magnet Resonance Res Med Sch Dept Radiol Minneapolis MN USA Univ Minnesota Med Sch Dept Radiat Oncol Minneapolis MN USA

Background This study was aimed to optimize the fluorodeoxyglucose (FDG)-administered dose and scan time based on patient specifications using a highly sensitive five-ring bismuth germanium oxide (BGO)-based positron emission tomography/computed tomography (PET/CT) scanner (Discovery IQ).Methods We retrospectively analyzed 101 whole-body F-18-FDG PET/CT images. Patient data were reconstructed using ordered subset expectation maximization with resolution recovery algorithms (OSEM + SharpIR). Signal-to-noise ratio (SNR) was calculated for each patient, standardized to SNRnorm , and plotted against three body index parameters (weight, body mass index, and lean body mass). Two professional physicians blindly examined image quality at different patient time per bed positions to determine the minimum acceptable quality. To select images of acceptable quality, the noise index parameter was also measured. A new dose-time product (DTP) was established for each patient, and a predicted injected dose was *** We found an almost linear association between patient weight and normalized SNR, and patient weight had the highest R-2 in the fitting. The redesigned DTP can reduce results by approximately 74 and 38% compared with ordinary DTP for 80- and 160-s scan durations. The new dose regimen formula was found to be DTP = c/t x m(1.24) , where m is the patient weight, t is the scan time per bed position, and c is 1.8 and 4.3 for acceptable and higher confidence states, respectively, in Discovery IQ PET/*** Patient weight is the best clinical parameter for the implementation of F-18-FDG PET/CT image quality assessment. A new dose-time regimen based on body weight was proposed for use in highly sensitive five-ring BGO PET-CT scanners to significantly reduce the injection dose and scan times while maintaining sufficient image quality for diagnosis.

关键词： dose optimization BGO-based positron-emission tomography dependency reconstruction algorithm

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The use of a proposed updated EARL harmonization of ¹⁸F-FDG PET-CT in patients with lymphoma yields significant differences in Deauville score compared with current EARL recommendations

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EJNMMI RESEARCH 2019年第1期9卷 65-65页

作者： Ly, John Minarik, David Edenbrandt, Lars Wollmer, Per Tragardh, Elin Kristianstad Hosp Dept Radiol Kristianstad Sweden Lund Univ Dept Translat Med Malmo Sweden Skane Univ Hosp Radiat Phys Malmo Sweden Lund Univ Malmo Sweden Sahlgrens Univ Hosp Dept Clin Physiol & Nucl Med Reg Vastra Gotaland Gothenburg Sweden Skane Univ Hosp Dept Clin Physiol & Nucl Med Malmo Sweden Lund Univ Wallenberg Ctr Mol Med Lund Sweden

BackgroundThe Deauville score (DS) is a clinical tool, based on the comparison between lesion and reference organ uptake of F-18-fluorodeoxyglucose (FDG), used to stratify patients with lymphoma into categories reflecting their disease status. With a plethora of positron emission tomography with computed tomography (PET-CT) hard- and software algorithms, standard uptake value (SUV) in lesions and reference organs may differ which affects DS classification and therefore medical treatment. The EANM Research Ltd. (EARL) harmonization program from the European Association of Nuclear Medicine (EANM) partly mitigates this issue, but local preferences are common in clinical practice. We have investigated the discordance in DS calculated from patients with lymphoma referred for F-18-FDG PET-CT reconstructed with three different algorithms: the newly introduced block-sequential regularization expectation-maximization algorithm commercially sold as Q. Clear (QC, GE Healthcare, Milwaukee, WI, USA), compliant with the newly proposed updated EARL recommendations, and two settings compliant with the current EARL recommendations (EARL(lower) and EARL(upper), representing the lower and upper limit of the EARL recommendations).MethodsFifty-two patients with non-Hodgkin and Hodgkin lymphoma were included (18 females and 34 males). Segmentation of mediastinal blood pool and liver were semi-automatically performed, whereas segmentation of lesions was done manually. From these segmentations, SUVmax and SUVpeak were obtained and DS *** was a significant difference in DS between the QC algorithm and EARL(lower)/EARL(upper) (p<0.0001 for both) but not between EARL(lower) and EARL(upper) (p=0.102) when SUVmax was used. For SUVpeak, there was a significant difference between QC and EARL(lower) (p=0.001), but not for QC vs EARL(upper) (p=0.071) or EARL(lower) vs EARL(upper) (p=0.102). Five non-responders (DS 4-5) for QC were classified as responders (DS 1-3) when EARL(lowe

关键词： Deauville score reconstruction algorithm Lymphoma EARL PET

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Review of Ultra-Wideband Communication Technology Based on Compressed Sensing

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Procedia Engineering 2012年 29卷 3262-3266页

作者： Xiaoli Lv Fengming Bai College of Electronics and Information Engineering Changchun University of Science and Technology Weixing Road No.7089JilinChangchun 130022China College of Electrical and Information Engineering Changchun Institute of Technology Kuanping Road No.395JilinChangchun 130012China

According to Nyquist sampling theorem, the traditional sampling frequency of signal not less than twice the highest frequency. However, due to the higher frequency band and high-bandwidth of the Ultra-wideband signal, making the sampling rate is too high to achieve. Compressed Sensing theory provides a theory basis to cut into sampling rate possibility, and introduces a solution to deal with bottlenecks of digital-analog conversion technology on Ultra-wideband. Compressed Sensing can reconstruct the original signal accurately with lower Nyquist sampling. It has broad application prospects in the Ultra-wideband communications. This paper introduces the basic theory and applications of Compressed Sensing and Ultra-wideband, and look forward to the prospects for the study.

关键词： Compressed Sensing(CS) Ultra-wideband(UWB) Sparse Measurement Matrix reconstruction algorithm

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Corrosion Monitoring Method of Porous Aluminum Alloy Plate Hole Edges Based on Piezoelectric Sensors

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SENSORS 2019年第5期19卷 1106-1106页

作者： Dai, Wei Wang, Xiangyu Zhang, Meng Zhang, Weifang Wang, Rongqiao Beihang Univ Sch Reliabil & Syst Engn 37 Xueyuan Rd Beijing 100191 Peoples R China Beihang Univ Sch Energy & Power Engn 37 Xueyuan Rd Beijing 100191 Peoples R China Beihang Univ Collaborat Innovat Ctr Adv Aeroengine 37 Xueyuan Rd Beijing 100191 Peoples R China

Corrosion damage to the aircraft structure can significantly reduce the safety performance and endanger flight safety. Especially when the corrosion occurs in a stress concentration region, such as hole edges, it can easily threaten the entire structure. In this paper, an on-line imaging qualitative monitoring algorithm based on piezoelectric sensors is proposed for detecting hole edge corrosion damage of porous aluminum alloy structures. The normalized amplitude is used to characterize the correlation between the initial Lamb wave signal and the damage signal, which is as an image reconstruction parameter in the algebraic iterative probability reconstruction algorithm. Moreover, a homogenization algorithm is proposed to process the reconstruction results. The experimental results of single hole and double hole corrosion for porous aluminum alloy plate show that the method can effectively achieve the location and quantification of corrosion damage to one and two holes of the porous structure.

关键词： corrosion damage detection reconstruction algorithm Lamb wave porous aluminum alloy plate

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Elementary introduction of the reconstruction of nonuniformly sampled signals in azimuth of displaced phase centres multi-beam in azimuth spaceborne synthetic aperture radar

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Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology 2004年第SUPPL.期26卷 195-201页

作者： Chen, Zhi-Yuan Qi, Xiang-Yang Li, Jian-Xiong Institute of Electronics Chinese Academy of Sciences Beijing 100080 China

We first analyzed the characteristics of the nonuniformly sampled signals in azimuth of displaced phase centres multi-beam in azimuth spaceborne synthetic aperture radar when its PRF is not equal to the ideal value. T... 详细信息

关键词： Multi-beam in azimuth Nonuniformly sampled signals reconstruction algorithm Synthetic aperture radar (SAR)

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Fourier diffraction theorem for diffusion-based thermal tomography

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JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 2006年第46期39卷 14379-14395页

作者： Baddour, Natalie Univ Ottawa Dept Mech Engn Ottawa ON K1N 6N5 Canada

There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging.

关键词： DEFECT DETECTION THERMOGRAPHY reconstructionS Tomography Fourier Nondestructive Testing Thermal INSPECTION SYSTEM Defect detection Heat waves Thermography diffraction Theorem reconstruction algorithm

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Imaging the complex conductivity distribution in electrical impedance tomography

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IFAC Proceedings Volumes 2003年第15期36卷 73-76页

作者： Peimin Yan Yulong Mo Dept. of Communication Engineering. Shanghai Univ. Shanghai China. 200072

Electrical impedance tomography (EIT) uses current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. The present reconstruction algorithm using sensitivity matrix images the complex conductivity distribution due to the permittivity distribution inside the body. A finite element model (FEM) with mesh refinement is used to solve the forward problem in order to improve image resolution. Computer simulations showed that the full information contained in the complex tissue conductivity (real and imaginary components) could be obtained by this method.

关键词： Electrical impedance tomography (EIT) Complex conductivity Finite element Mesh refinement Sensitivity matrix reconstruction algorithm

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Moment quantization and (A-adic) discrete-continuous wavelet transform theory

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JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 1999年第46期32卷 8111-8128页

作者： Handy, CR Murenzi, R Clark Atlanta Univ Dept Phys Atlanta GA 30314 USA Clark Atlanta Univ Ctr Theoret Studies Phys Syst Atlanta GA 30314 USA

We establish how moment quantization directly leads to a complete (A-adic) discrete-continuous wavelet transform theory in contrast to the approximate reconstruction methods published earlier.

关键词： Quantization Moment of force theories mathematics wavelet transforms reconstruction algorithm

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