Article
Geochemistry & Geophysics
Fan Li, Jianjun Gao, Mauricio D. Sacchi, Jun Lu, Yun Wang, Haifeng Chen, Chaolin Li
Summary: Multicomponent seismic exploration is attracting attention in the search for and identification of subtle oil and gas reservoirs. However, the sparse and irregular sampling problems encountered in single-component acquisition also apply to multicomponent seismic data acquisition. In this study, we propose a new vector Projection Onto Convex Sets (POCS) method with biquaternion Fourier transform to reconstruct irregularly missing traces of 3-D and three-component (3-D-3C) seismic data. The proposed method performs in the frequency domain and maintains the conjugate symmetry property of the biquaternion data, demonstrating its effectiveness and superiority over existing methods.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Mathematics, Applied
Denghui Wu, Zhen-Hui Bu
Summary: This paper introduces a new concept of (p, q)-projection body, discusses a variant of the L-p Shephard problem, and answers two parts of the question by connecting with L-p projection body and Levy's embedding L-p.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Stefan Steinerberger
Summary: The Kaczmarz method is used for solving linear systems by selecting equations based on rows, allowing for faster convergence by adjusting the p-value. As p approaches infinity, the method de-randomizes and sheds light on why the maximal correction method is effective.
MATHEMATICS OF COMPUTATION
(2021)
Article
Engineering, Electrical & Electronic
Shuya Zhang, Fengchun Tian, James A. Covington, Hantao Li, Leilei Zhao, Ran Liu, Junhui Qian, Bei Liu
Summary: An effective calibration method for e-nose sensors based on POCS and ELM method is proposed in order to solve the drift problem under long-term working conditions. Isopropanol and acetone gases were chosen for training, and experiments show the effectiveness of the proposed calibration method.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2021)
Article
Optics
Mingzhu Wan, Lingbao Kong
Summary: In this paper, a single-shot high dynamic range 3D measurement method combining FPP with deep learning is proposed. The method solves the overexposure problem in highly reflective areas by using a self-attention mechanism and improves measurement accuracy by predicting wrapped phase maps and absolute phase maps. Experiments showed that the proposed method accurately predicted the optimal exposure time under single-shot condition.
Article
Engineering, Aerospace
Jie Zhang, Jin Liu, Xin Ma, Zhi-wei Kang, Zhen-ni Wang
Summary: The solar spectrum velocimetry method using mirror NDFT-CS achieves high accuracy in real time by matching the measured solar spectrum with a Doppler frequency-shift dictionary.
JOURNAL OF AEROSPACE ENGINEERING
(2021)
Article
Mathematics, Applied
Stefan Steinerberger
Summary: Randomized Kaczmarz is a simple iterative method for finding solutions of linear systems Ax = b, where the sequence of solutions converges to the singular vector corresponding to the smallest singular value of the matrix as the number of iterations approaches infinity. This method also allows for fast computation of vectors with small Rayleigh quotients.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Konrad Engel, Bastian Laasch
Summary: This paper investigates the modulus of Fourier transform of a convex polytope P on a hypersurface S in R^n with wavelength lambda, aiming to reconstruct P or compute its properties. The main analysis tool is an asymptotic formula for the Fourier transform of P as lambda approaches 0. The study is motivated by X-ray scattering of nanoparticles, where the Fourier transform of reflected beam wave vectors is measurable on a half sphere in experiments.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2022)
Article
Chemistry, Analytical
Bingquan Chen, Peng Shi, Yanhua Wang, Yongze Xu, Hongyang Ma, Ruirong Wang, Chunhong Zheng, Pengcheng Chu
Summary: This study proposes a method for determining the surface shape of translucent objects using a combination of projected laser-beam-based sinusoidal structured light and polarization technique. The theoretical analyses and experimental investigations confirm the accuracy and effectiveness of this approach in measuring and reconstructing translucent objects, even in the presence of background illumination.
Article
Optics
Lin Wu, Ziyang Zhang
Summary: Computer-generated holography can achieve arbitrary intensity distributions in space with the wavefront obtained. However, speckle noises continue to be a challenge. A new algorithm for hologram generation and a unique multiplexing scheme using a Fourier lens have been proposed in this work. This technology shows potential for doubling the capacity of current holographic systems and offers various interesting display applications.
Article
Engineering, Electrical & Electronic
Deyun Wei, Jun Yang
Summary: A novel estimation algorithm is proposed for non-uniform discrete Fourier transform (NUDFT) in this paper, which achieves compression of sparse signals and accurate detection of frequencies.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Madad Khan, Inamullah Khan, Aliya Fahmi, Saima Anis, Sohail Iqbal
Summary: In this paper, we introduced new operations and formulas of set theory for complex fuzzy sets (CFSs) and presented their basic results and examples. Additionally, we proposed an algorithm to identify a reference signal out of a large number of signals, enabling faster measurement of signal values using CFSs.
Article
Engineering, Electrical & Electronic
Fatma Hawary, Guillaume Boisson, Christine Guillemot, Philippe Guillotel
Summary: This paper explores the compressive sensing framework for overcoming the spatial-angular trade-off in light field acquisition. A novel method is proposed to reconstruct a full 4D light field from sparse data samples by utilizing sparse models in the 4D Fourier domain. Experimental results show significant performance improvements in both visual quality and signal-to-noise ratio compared to state-of-the-art compressive light field reconstruction methods.
SIGNAL PROCESSING-IMAGE COMMUNICATION
(2021)
Article
Chemistry, Multidisciplinary
Yiran Li, Hanlu Yang, Danfeng Xie, David Dreizin, Fuqing Zhou, Ze Wang
Summary: Recent years have witnessed a growing research interest in replacing the computationally intensive MR image reconstruction process with deep neural networks. The proposed hybrid DL image reconstruction method, combining a state-of-the-art deep learning network with a traditional data reconstruction algorithm, showed superior reconstruction results compared to other state-of-the-art DL-based methods and a traditional compressed sensing method.
APPLIED SCIENCES-BASEL
(2022)
Article
Geosciences, Multidisciplinary
Hormoz Izadi, Scott Keating
Summary: The Born series provides a framework for connecting earth model parameters and a wavefield characterized by perturbation around a known reference wavefield. The inverse scattering series provides both linear and nonlinear expressions for approximating earth model parameters. The linear expression accurately approximates the depth-varying velocity profile with low contrast, while the nonlinear expression is required for higher accuracy.
JOURNAL OF APPLIED GEOPHYSICS
(2023)