The Experts below are selected from a list of 10950 Experts worldwide ranked by ideXlab platform
Wolfgang Hackbusch - One of the best experts on this subject based on the ideXlab platform.
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Convolution of hp-functions on locally refined grids
IMA Journal of Numerical Analysis, 2008Co-Authors: Wolfgang HackbuschAbstract:Usually, the fast evaluation of a Convolution integral ∫ ℝ f(y)g(x - y)dy requires that the functions f and g have a simple structure based on an equidistant grid in order to apply the fast Fourier transform. Here, we discuss the efficient performance of the Convolution of hp-functions in certain locally refined grids. More precisely, the Convolution Result is projected into some given hp-space (Galerkin approximation). The overall cost is O(p 2 N log N), where N is the sum of the dimensions of the subspaces containing f , g and the Resulting function, while p is the maximal polynomial degree.
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fast projected Convolution of piecewise linear functions on non equidistant grids
2008Co-Authors: Wolfgang HackbuschAbstract:Usually, the fast evaluation of a Convolution integral f ℝ f(y)g(x−y)dy requires that the functions f, g are discretised on an equidistant grid in order to apply FFT. Here we discuss the efficient performance of the Convolution in locally refined grids. More precisely, f and g are assumed to be piecewise linear and the Convolution Result is projected into the space of linear functions in a given locally refined grid. Under certain conditions, the overall costs are still O(N logN), where N is the sum of the dimensions of the subspaces containing f, g and the Resulting function.
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Fast and exact projected Convolution for non-equidistant grids
Computing, 2007Co-Authors: Wolfgang HackbuschAbstract:Usually, the fast evaluation of a Convolution integral $$\int_{{\mathbb{R}}}f(y)g(x-y)\mathrm{d}y$$ requires that the functions f , g are discretised on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the Convolution in locally refined grids. More precisely, the Convolution Result is projected into some given locally refined grid (Galerkin approximation). Under certain conditions, the overall costs are still $${\mathcal{O}}(N\log N),$$ where N is the sum of the dimensions of the subspaces containing f , g and the Resulting function.
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Fast and Exact Projected Convolution of Piecewise Linear Functions on Non-equidistant Grids - Extended Version
2006Co-Authors: Wolfgang HackbuschAbstract:Usually, the fast evaluation of a Convolution integral ∫ R f(y)g(x − y)dy requires that the functions f, g are discretised on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the Convolution in locally refined grids. More precisely, f and g are assumed to be piecewise linear and the Convolution Result is projected into the space of linear functions in a given locally refined grid. Under certain conditions, the overall costs are still O(N logN), where N is the sum of the dimensions of the subspaces containing f , g and the Resulting function. AMS Subject Classifications: 44A35, 42A55
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Fast and Exact Projected Convolution for Non-equidistant Grids - Extended Version
2006Co-Authors: Wolfgang HackbuschAbstract:Usually, the fast evaluation of a Convolution integral ∫ R f(y)g(x − y)dy requires that the functions f, g are discretised on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the Convolution in locally refined grids. More precisely, the Convolution Result is projected into some given locally refined grid. Under certain conditions, the overall costs are still O(N logN), where N is the sum of the dimensions of the subspaces containing f , g and the Resulting function. AMS Subject Classifications: 44A35, 42A55
Jaeyoung Jang - One of the best experts on this subject based on the ideXlab platform.
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intermediate elemental image reconstruction for refocused three dimensional images in integral imaging by Convolution with δ function sequences
Optics and Lasers in Engineering, 2017Co-Authors: Hoon Yoo, Jaeyoung JangAbstract:Abstract We propose a novel approach for intermediate elemental image reconstruction in integral imaging. To reconstruct intermediate elemental images, we introduce a null elemental image whose pixels are all zero. In the proposed method a number of null elemental images are inserted into a given elemental image array. The elemental image array with null elemental images is convolved with the δ-function sequence. The Convolution Result shows that the proposed method provides an efficient structure to expand an elemental image array. The Resulting elemental image array from the proposed method can supply three-dimensional information for an object at a specific depth. In addition, the proposed method provides adjustable parameters, which can be utilized in design of integral imaging systems. The feasibility of the proposed method has been confirmed through preliminary experiments and theoretical analysis.
Wei Chen - One of the best experts on this subject based on the ideXlab platform.
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Frame-Independent and Parallel Method for 3D Audio Real-Time Rendering on Mobile Devices
MultiMedia Modeling, 2017Co-Authors: Yucheng Song, Xiaochen Wang, Ge Gao, Wei Chen, Cheng Yang, Weiping TuAbstract:As 3D audio is a fundamental medium of virtual reality (VR), 3D audio real-time rendering technique is essential for the implementation of VR, especially on the mobile devices. While constrained by the limited computational power, the computation load is too high to implement 3D audio real-time rendering on the mobile devices. To solve this problem, we propose a frame-independent and parallel method of framing Convolution, to parallelize process of 3D audio rendering using head-related transfer function (HRTF). In order to refrain from the dependency of overlap-add Convolution over the adjacent frames, the data of Convolution Result is added on the final Results of the two adjacent frames. We found our method could reduce the calculation time of 3D audio rendering significantly. The Results were 0.74 times, 0.5 times and 0.36 times the play duration of si03.wav (length of 27 s), with Snapdragon 801, Kirin 935 and Helio X10 Turbo, respectively.
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MMM (2) - Frame-Independent and Parallel Method for 3D Audio Real-Time Rendering on Mobile Devices
MultiMedia Modeling, 2016Co-Authors: Yucheng Song, Xiaochen Wang, Ge Gao, Cheng Yang, Wei ChenAbstract:As 3D audio is a fundamental medium of virtual reality (VR), 3D audio real-time rendering technique is essential for the implementation of VR, especially on the mobile devices. While constrained by the limited computational power, the computation load is too high to implement 3D audio real-time rendering on the mobile devices. To solve this problem, we propose a frame-independent and parallel method of framing Convolution, to parallelize process of 3D audio rendering using head-related transfer function (HRTF). In order to refrain from the dependency of overlap-add Convolution over the adjacent frames, the data of Convolution Result is added on the final Results of the two adjacent frames. We found our method could reduce the calculation time of 3D audio rendering significantly. The Results were 0.74 times, 0.5 times and 0.36 times the play duration of si03.wav (length of 27 s), with Snapdragon 801, Kirin 935 and Helio X10 Turbo, respectively.
Yue Chen - One of the best experts on this subject based on the ideXlab platform.
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Convolution forgetting curve model for repeated learning
Artificial Intelligence in Education, 2020Co-Authors: Yanlu Xie, Yue ChenAbstract:Most mathematical forgetting curve models can fit the forgetting data well under the condition of one-time learning, rather than repeated learning. In the paper, a Convolution model of the forgetting curve is proposed to simulate the memory process during learning. In this model, the memory ability (i.e. the central procedure in the working memory model) and learning material (i.e. the input in the working memory model) is regarded as the system function and the input function, respectively. The status of forgetting (i.e. the output in the working memory model) is regarded as output function or the Convolution Result of the memory ability and learning material. The model is applied to simulate the forgetting curves in different situations. The Results show that the model is able to simulate the forgetting curves not only in one-time learning conditions but also in multi-times conditions. The model is further verified in the experiments of Mandarin tone learning for Japanese learners. And the predicted curve fits well with the test points.
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Convolution Forgetting Curve Model for Repeated Learning
arXiv: Neurons and Cognition, 2019Co-Authors: Yanlu Xie, Yue ChenAbstract:Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a Convolution model of forgetting curve is proposed to simulate the memory process during learning. In this model, the memory ability (i.e. the central procedure in the working memory model) and learning material (i.e. the input in the working memory model) is regarded as the system function and the input function, respectively. The status of forgetting (i.e. the output in the working memory model) is regarded as output function or the Convolution Result of the memory ability and learning material. The model is applied to simulate the forgetting curves in different situations. The Results show that the model is able to simulate the forgetting curves not only in one time learning condition but also in multi-times condition. The model is further verified in the experiments of Mandarin tone learning for Japanese learners. And the predicted curve fits well on the test points.
Yucheng Song - One of the best experts on this subject based on the ideXlab platform.
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Frame-Independent and Parallel Method for 3D Audio Real-Time Rendering on Mobile Devices
MultiMedia Modeling, 2017Co-Authors: Yucheng Song, Xiaochen Wang, Ge Gao, Wei Chen, Cheng Yang, Weiping TuAbstract:As 3D audio is a fundamental medium of virtual reality (VR), 3D audio real-time rendering technique is essential for the implementation of VR, especially on the mobile devices. While constrained by the limited computational power, the computation load is too high to implement 3D audio real-time rendering on the mobile devices. To solve this problem, we propose a frame-independent and parallel method of framing Convolution, to parallelize process of 3D audio rendering using head-related transfer function (HRTF). In order to refrain from the dependency of overlap-add Convolution over the adjacent frames, the data of Convolution Result is added on the final Results of the two adjacent frames. We found our method could reduce the calculation time of 3D audio rendering significantly. The Results were 0.74 times, 0.5 times and 0.36 times the play duration of si03.wav (length of 27 s), with Snapdragon 801, Kirin 935 and Helio X10 Turbo, respectively.
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MMM (2) - Frame-Independent and Parallel Method for 3D Audio Real-Time Rendering on Mobile Devices
MultiMedia Modeling, 2016Co-Authors: Yucheng Song, Xiaochen Wang, Ge Gao, Cheng Yang, Wei ChenAbstract:As 3D audio is a fundamental medium of virtual reality (VR), 3D audio real-time rendering technique is essential for the implementation of VR, especially on the mobile devices. While constrained by the limited computational power, the computation load is too high to implement 3D audio real-time rendering on the mobile devices. To solve this problem, we propose a frame-independent and parallel method of framing Convolution, to parallelize process of 3D audio rendering using head-related transfer function (HRTF). In order to refrain from the dependency of overlap-add Convolution over the adjacent frames, the data of Convolution Result is added on the final Results of the two adjacent frames. We found our method could reduce the calculation time of 3D audio rendering significantly. The Results were 0.74 times, 0.5 times and 0.36 times the play duration of si03.wav (length of 27 s), with Snapdragon 801, Kirin 935 and Helio X10 Turbo, respectively.