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fast BET Based on Pre-Processing Evolution Using Global Mean Inter-Vertex Distance of Deformable Surface for MRI Brain Extraction

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INTERNATIONAL JOURNAL OF IMAGE AND GRAPHICS 2024年第0期

作者： Son, ChangIl Ma, JongSu Bong, IlRyong Yu, NamChol Kim Chaek Univ Technol Biomed Engn Fac Dept Biomed Engn Gyogu 60 Pyongyang North Korea PyongSong Univ Educ Phys Fac Dept Biophys Dumu 20 Pyongsong North Korea Sariwon Inst Technol Phys Fac Dept Biophys Sangmae 25 Sariwon North Korea Kim Chaek Univ Technol Elect Engn Fac Dept Elect Mat Gyogu 60 Pyongyang North Korea

As a method based on the deformable surface evolution, brain extraction tools (BET) is widely used for brain extraction on cranial 3D magnetic resonance (MR) images. BET iteratively applies an evolution model depending on local parameters to the deformable surface until it reaches the brain border. In this paper, we propose a modified BET based on the fast model introducing a global parameter, the global mean inter-vertex distance of deformable surface. The surface evolution consists of two steps driven by two models: pre-processing step by the fast model and major step by the original model. We demonstrated our method in the experiments with T1-weighted and diffusion weighted MR images of 19 normal subjects. The modified BET converged within 300 iterations less than half of about 1000 iterations in the original BET, while reducing substantially the false negative regions and self-intersections. The proposed method may be efficient for high resolution images and large-scale studies.

关键词： Magnetic resonance imaging brain extraction tools deformable surface global parameter global mean inter-vertex distance fast algorithm

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Computationally-Efficient Overdetermined Blind Source Separation Based on Iterative Source Steering

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IEEE SIGNAL PROCESSING LETTERS 2022年 29卷 927-931页

作者： Du, Yicheng Scheibler, Robin Togami, Masahito Yoshii, Kazuyoshi Kawahara, Tatsuya Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan LINE Corp Tokyo 1600004 Japan

This paper describesa computationally-efficient optimization algorithm for the blind source separation (BSS) of overdetermined mixtures. In the determined case, a matrix-inversion-free iterative source steering (ISS) algorithm has been proposed for estimating a square demixing matrix as a computationally-efficient alternative to the popular iterative projection (IP) algorithm. The IP algorithm is based on source-wise (i.e., row-wise) updates of the demixing matrix, and lends itself naturally to an extension to overdetermined independent vector analysis (IVA) called OverIVA. In contrast, the ISS algorithm changes the whole demixing matrix at every update, making its extension to the overdetermined case non-trivial. In this paper, we propose a modified ISS algorithm for OverIVA fully exploiting the computational savings of ISS. We also derive an overdetermined extension of independent low-rank matrix analysis (OverILRMA) with the modified ISS algorithm. Experimental results showed that the proposed ISS-based OverIVA and OverILRMA were comparable or superior to the conventional IP-based counterparts in speech separation performance while achieving lower computational cost.

关键词： Signal processing algorithms IP networks Iterative algorithms Blind source separation Parameter estimation Microphones Cost function Overdetermined blind source separation independent vector analysis fast algorithm

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A fast Calculation Method of Gas Infrared Radiation Characteristics at High Temperature based on Radial Basis Function Neural Network

A Fast Calculation Method of Gas Infrared Radiation Characte...

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Optoelectronics Global Conference (OGC)

作者： Meng, Xiaying Du, Jun Wang, Biao Zhang, Yutao Gu, Dandan Qiu, Jian Sci & Technol Electromagnet Scattering Lab Shanghai Peoples R China Aero Engine Corp China Commercial Aircraft Engine Shanghai Peoples R China

ISBN: (纸本)9781665431941

The radiation characteristics of high temperature gas are of great significance for infrared target detection. In this paper, a calculation method of high temperature gas radiation characteristics with high calculation efficiency is proposed. The calculation model of CO2 absorption coefficient at 2001-2450 cm(-1) band is established by using radial basis function neural network (RBFNN). In RBFNN model, the most accurate line by line (LBL) method is utilized to generate training samples. The input parameters are gas temperature, pressure and component concentration, and the output parameter is absorption coefficient. The results show that, compared with LBL method, RBFNN model has higher accuracy and is insensitive to input. After RBFNN training, RBFNN has higher computational efficiency while ensuring computational accuracy.

关键词： gas infrared radiation radial basis function neural network fast algorithm absorption coefficient

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Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions

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COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 2021年第4期21卷 913-928页

作者： Shen, Jinye Stynes, Martin Zhi-Zhong Sun Beijing Computat Sci Res Ctr Appl & Computat Math Div Beijing 100193 Peoples R China Southwestern Univ Finance & Econ Inst Math Sch Econ Math Chengdu 611130 Sichuan Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China

A time-fractional initial-boundary value problem of wave type is considered, where the spatial domain is (0, 1)(d) for some d is an element of {1, 2, 3}. Regularity of the solution u is discussed in detail. Typical solutions have a weak singularity at the initial time t = 0: while u and u(t) are continuous at t = 0, the second-order derivative u(tt) blows up at t = 0. To solve the problem numerically, a finite difference scheme is used on a mesh that is graded in time and uniform in space with the same mesh size h in each coordinate direction. This scheme is generated through order reduction: one rewrites the differential equation as a system of two equations using the new variable v := u(t);then one uses a modified L1 scheme of Crank-Nicolson type for the driving equation. A fast variant of this finite difference scheme is also considered, using a sum-of-exponentials (SOE) approximation for the kernel function in the Caputo derivative. The stability and convergence of both difference schemes are analysed in detail. At each time level, the system of linear equations generated by the difference schemes is solved by a fast Poisson solver, thereby taking advantage of the fast difference scheme. Finally, numerical examples are presented to demonstrate the accuracy and efficiency of both numerical methods.

关键词： Multi-Dimensional Time-Fractional Wave Equation Weak Singularity fast algorithm Difference Scheme Convergence

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Reconstruction of shear force in Atomic Force Microscopy from measured displacement of the cone-shaped cantilever tip

MATHEMATICS IN ENGINEERING

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MATHEMATICS IN ENGINEERING 2024年第1期6卷 137-154页

作者： Hasanov, Alemdar Kawano, Alexandre Baysal, Onur Kocaeli Univ Dept Math Kocaeli Turkiye Univ Sao Paulo Escola Politecn BR-05508900 Sao Paulo Brazil Univ Malta Dept Math Msida Malta

We present a new comprehensive mathematical model of the cone-shaped cantilever tipsample interaction in Atomic Force Microscopy (AFM). The importance of such AFMs with coneshaped cantilevers can be appreciated when its ability to provide high-resolution information at the nanoscale is recalled. It is an indispensable tool in a wide range of scientific and industrial fields. The interaction of the cone-shaped cantilever tip with the surface of the specimen (sample) is modeled by the damped Euler-Bernoulli beam equation rho A(x)utt +mu(x)ut + (r(x)uxx + kappa(x)uxxt)xx = 0, (x, t) E (0, euro) x (0, T), subject to the following initial, u(x, 0) = 0, ut(x, 0) = 0 and boundary, u(0, t) = 0, ux(0, t) = 0, (r(x)uxx(x, t) + kappa(x)uxxt)x=e = M(t), (-(r(x)uxx + kappa(x)uxxt)x)x=e = g(t) conditions, where M(t) := 2h cos theta g(t)/pi is the moment generated by the transverse shear force g(t). Based on this model, we propose an inversion algorithm for the reconstruction of an unknown shear force in the AFM cantilever. The measured displacement nu(t) := u(euro, t) is used as additional data for the reconstruction of gradient formula for the Frechet derivative of the cost functional is derived via the weak solution contained in this formula. This enables us to construct a gradient based numerical algorithm for the reconstructions of the shear force from noise free as well as from random noisy measured output nu(t). Computational experiments show that the proposed algorithm is very fast and robust. This creates the basis for developing a numerical "gadget" for computational experiments with generic AFMs.

关键词： Atomic Force Microscopy cone-shaped cantilever reconstruction of shear force damped Euler-Bernoulli cantilever beam inverse problem gradient formula fast algorithm

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Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions

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APPLIED MATHEMATICS AND COMPUTATION 2022年 430卷

作者： Zhang, Jiali Fang, Zhi-Wei Sun, Hai-Wei Univ Macau Dept Math Macau Peoples R China Foshan Univ Sch Math & Big Data Foshan Peoples R China

A robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs) is developed, superiorly handling the cases of small or vanishing lower bound of the VO function. The fast finite difference scheme sharp decreases the storage requirement and computational complexity. Significantly, the error estimate for the proposed scheme is studied without any regularity assumptions of the true solution. Numerical experiments are tested to verify the effectiveness of the proposed method. (C) 2022 Elsevier Inc. All rights reserved.

关键词： Variable-order Caputo fractional derivative fast algorithm Exponential-sum-approximation method

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KERNEL-BASED IMAGE FILTERING: fast algorithmS AND APPLICATIONS 26

KERNEL-BASED IMAGE FILTERING: FAST ALGORITHMS AND APPLICATIO...

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26th IEEE International Conference on Image Processing (ICIP)

作者： Ghosh, Sanjay Chaudhury, Kunal N. Indian Inst Sci Dept Elect Engn Bengaluru India

ISBN: (纸本)9781538662496

Image filtering is a fundamental preprocessing task in computer vision and image processing. While the dominant applications of kernel filtering are enhancement and denoising, it can also be used as a powerful regularizer for image reconstruction. In general, the brute-force implementations of kernel filtering is prohibitively expensive. They are often too slow for real-time applications. In the first half of the thesis, we propose fast algorithms for bilateral filtering (BLF) and nonlocal means (NLM). In particular, we demonstrate that by using the Fourier approximation of the underlying kernel, we can obtain state-of-the-art fast algorithms for BLF of grayscale images. We next extend the idea for fast filtering of color images, which involves the approximation of a three-dimensional kernel. We next propose a fast separable formulation for NLM of grayscale images. In the second half of the dissertation, we turn to some applications of kernel filtering. We introduce a scale-adaptive variant of BLF that is used for suppressing fine textures in images. We develop a fast implementation of a symmetrized variant of NLM that is used for regularization (i.e., as a prior) within the plug-and-play framework for image restoration. The core idea can be extended to other forms of kernel filtering.

关键词： low-light enhancement retinex bilateral filter Fourier approximation fast algorithm

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TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation

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MATHEMATICS AND COMPUTERS IN SIMULATION 2021年 181卷 117-137页

作者： Gao, Xinghua Yin, Baoli Li, Hong Liu, Yang Inner Mongolia Univ Sch Math Sci Hohhot 010021 Peoples R China

In this paper, we consider a fast algorithm to calculate a two-dimensional nonlinear time distributed-order and space fractional diffusion equation, which is called the time two-mesh (TT-M) finite element (FE) method. In time, the TT-M algorithm combined with both the implicit second-order sigma backward difference formula and Crank-Nicolson scheme for computing the numerical solution at time t1 is used to speed up the calculation. At the same time, the spatial direction is approximated by the FE method. The detailed analyses of stability and error are also given, and the second-order time convergence accuracy can be arrived at. Finally, some numerical examples are shown to illustrate the effectiveness of our numerical method. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： fast algorithm TT-M FE method Second-order sigma backward difference scheme Crank-Nicolson scheme

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fast difference scheme for a tempered fractional Burgers equation in porous media

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APPLIED MATHEMATICS LETTERS 2022年第0期132卷

作者： Wang, Haihong Li, Can Xian Univ Technol Sch Math & Stat Dept Appl Math Xian 710054 Shaanxi Peoples R China

In this paper we present a fast difference scheme for a tempered fractional Burgers equation. The model arises in describing the wave propagation in porous media with the power law and exponential attenuation. To avoid solving the discrete algebraic system by iteration, we present a linearized difference approximation for the nonlinear term. To reduce the numerical computational cost, we propose a fast algorithm for tempered fractional derivative. The fast algorithm is based on the summation of exponentials technique which is developed in Jiang et al. (2017). The theoretical analysis shows that our fast difference scheme is unconditionally stable and convergence. Numerical results demonstrate a competitive performance of the proposed fast difference scheme in comparison to the direct difference scheme.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Time fractional Burgers equation Tempered fractional derivative fast algorithm Stability and convergence

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Gohberg-Semencul Factorization-Based fast Implementation of Sparse Bayesian Learning With a Fourier Dictionary

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2022年 60卷 1页

作者： Dai, Fengzhou Wang, Yuanyuan Hong, Ling Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Peoples R China Shaanxi Normal Univ Key Lab Modern Teaching Technol Minist Educ Xian 710119 Peoples R China Shaanxi Normal Univ Sch Comp Sci Xian 710119 Peoples R China

Sparse Bayesian learning (SBL) is a popular and robust algorithm for sparse signal reconstruction (SSR). Unfortunately, the SBL algorithm suffers from heavy computational complexity when it is implemented directly since the inversion and multiplying operations of the estimation of the covariance matrix are involved in each iteration, which is proportional to the cube of the observed data length and thus prevents it solving large-scale problems. In many applications, such as radar imaging and array signal processing, the signal to be recovered is sparse in the Fourier dictionary. In this article, we propose an efficient implementation method for the Fourier dictionary-based SBL (FD-SBL). In the case that the Fourier dictionary is adopted, the estimation of the covariance matrix is a Toeplitz matrix for 1-D data or a Toeplitz-block-Toeplitz (TBT) matrix for 2-D data during the FD-SBL iterations. By utilizing this property, we employ the Gohberg-Semencul (G-S)-type factorization to accelerate the implementation of FD-SBL. To be noted, there is no approximation in our proposed method, and the computational cost is reduced by several orders of magnitude compared with the direct implementation of SBL. Finally, the experimental results verify the effectiveness of the proposed method.

关键词： Dictionaries Signal processing algorithms Sparse matrices Bayes methods Estimation Covariance matrices Two dimensional displays fast algorithm Fourier dictionary Gohberg-Semencul factorization sparse Bayesian learning

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