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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
Communications in Computational Physics, 2019We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) --- DNNs often fit target functions from low to high frequencies --- on high-dimensional
Zhi-Qin John Xu +4 more
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Fractional Fourier Analysis Using the Möbius Inversion Formula
IEEE Transactions on Signal Processing, 2019Compared with the Fourier analysis, the fractional Fourier analysis is more suitable to process linear frequency modulation type non-stationary functions.
Hongxia Miao, Feng Zhang, R. Tao
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Fourier Analysis and Fourier Transform
2017The origins of Fourier analysis in science can be found in Ptolemy’s decomposing celestial orbits into cycles and epicycles and Pythagoras’ decomposing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J.
Aparna Vyas, Soohwan Yu, Joonki Paik
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Single-Image Depth Estimation Based on Fourier Domain Analysis
2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018We propose a deep learning algorithm for single-image depth estimation based on the Fourier frequency domain analysis. First, we develop a convolutional neural network structure and propose a new loss function, called depth-balanced Euclidean loss, to ...
Jaehan Lee +3 more
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Fourier Analysis and Nonlinear Partial Differential Equations
, 2011H. Bahouri, J. Chemin, R. Danchin
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Improved cellulose X-ray diffraction analysis using Fourier series modeling
Cellulose, 2020W. Yao, Yu-Ching Weng, Jeffery Catchmark
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Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry
, 1982M. Takeda, Hideki Ina, Seiji Kobayashi
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