We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks an...We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency modes.We formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the eigenfunctions.Furthermore,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of eigenpairs.The effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video sequence.Our results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.展开更多
Traditional hyperspectral imaging(HI)systems are constrained by a limited depth of field(DoF),necessitating refocusing for any out-of-focus objects.This requirement not only slows down the imaging speed but also compl...Traditional hyperspectral imaging(HI)systems are constrained by a limited depth of field(DoF),necessitating refocusing for any out-of-focus objects.This requirement not only slows down the imaging speed but also complicates the system architecture.It is challenging to trade off among speed,resolution,and DoF within an ultrasimple system.While some studies have reported advancements in extending DoF,the improvements remain insufficient.To address this challenge,we propose a novel,to our knowledge,differentiable framework that integrates an extended DoF(E-DoF)wave propagation model and an achromatic hyperspectral reconstructor powered by deep learning.Through rigorous experimental validation,we have demonstrated that the compact HI system is capable of snapshot capturing of high-fidelity images with an exceptional DoF reaching approximately 5 m,marking a significant improvement of over three orders of magnitude.Additionally,the system achieves over 90%spectral accuracy without aberration,nearly doubling the accuracy performance of existing methods.An asymmetric freeform surface design is introduced for diffractive optical elements,enabling dual functionality with design freedom and E-DoF.The sparse prior conditions for spatial texture and spectral features of hyperspectral cubic data are integrated into the reconstruction network,effectively mitigating texture blurring and chromatic aberration.It foresees that the optimal strategy for achromatic E-DoF can be adopted into other optical systems such as polarization imaging and depth measurement.展开更多
In some image classification tasks, similarities among different categories are different and the samples are usually misclassified as highly similar categories. To distinguish highly similar categories, more specific...In some image classification tasks, similarities among different categories are different and the samples are usually misclassified as highly similar categories. To distinguish highly similar categories, more specific features are required so that the classifier can improve the classification performance. In this paper, we propose a novel two-level hierarchical feature learning framework based on the deep convolutional neural network(CNN), which is simple and effective. First, the deep feature extractors of different levels are trained using the transfer learning method that fine-tunes the pre-trained deep CNN model toward the new target dataset. Second, the general feature extracted from all the categories and the specific feature extracted from highly similar categories are fused into a feature vector. Then the final feature representation is fed into a linear classifier. Finally, experiments using the Caltech-256, Oxford Flower-102, and Tasmania Coral Point Count(CPC) datasets demonstrate that the expression ability of the deep features resulting from two-level hierarchical feature learning is powerful. Our proposed method effectively increases the classification accuracy in comparison with flat multiple classification methods.展开更多
基金Project supported by the U.S.Department of Energy under the Advanced Scientific Computing Research Program(No.DE-SC0019116)the U.S.Air Force Office of Scientific Research(No.AFOSR FA9550-20-1-0060)。
文摘We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency modes.We formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the eigenfunctions.Furthermore,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of eigenpairs.The effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video sequence.Our results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.
基金Youth Innovation Promotion Association of the Chinese Academy of Sciences(2022246)Shanghai Sailing Program(22YF1454800,20YF145480)。
文摘Traditional hyperspectral imaging(HI)systems are constrained by a limited depth of field(DoF),necessitating refocusing for any out-of-focus objects.This requirement not only slows down the imaging speed but also complicates the system architecture.It is challenging to trade off among speed,resolution,and DoF within an ultrasimple system.While some studies have reported advancements in extending DoF,the improvements remain insufficient.To address this challenge,we propose a novel,to our knowledge,differentiable framework that integrates an extended DoF(E-DoF)wave propagation model and an achromatic hyperspectral reconstructor powered by deep learning.Through rigorous experimental validation,we have demonstrated that the compact HI system is capable of snapshot capturing of high-fidelity images with an exceptional DoF reaching approximately 5 m,marking a significant improvement of over three orders of magnitude.Additionally,the system achieves over 90%spectral accuracy without aberration,nearly doubling the accuracy performance of existing methods.An asymmetric freeform surface design is introduced for diffractive optical elements,enabling dual functionality with design freedom and E-DoF.The sparse prior conditions for spatial texture and spectral features of hyperspectral cubic data are integrated into the reconstruction network,effectively mitigating texture blurring and chromatic aberration.It foresees that the optimal strategy for achromatic E-DoF can be adopted into other optical systems such as polarization imaging and depth measurement.
基金Project supported by the National Natural Science Foundation of China(No.61379074)the Zhejiang Provincial Natural Science Foundation of China(Nos.LZ12F02003 and LY15F020035)
文摘In some image classification tasks, similarities among different categories are different and the samples are usually misclassified as highly similar categories. To distinguish highly similar categories, more specific features are required so that the classifier can improve the classification performance. In this paper, we propose a novel two-level hierarchical feature learning framework based on the deep convolutional neural network(CNN), which is simple and effective. First, the deep feature extractors of different levels are trained using the transfer learning method that fine-tunes the pre-trained deep CNN model toward the new target dataset. Second, the general feature extracted from all the categories and the specific feature extracted from highly similar categories are fused into a feature vector. Then the final feature representation is fed into a linear classifier. Finally, experiments using the Caltech-256, Oxford Flower-102, and Tasmania Coral Point Count(CPC) datasets demonstrate that the expression ability of the deep features resulting from two-level hierarchical feature learning is powerful. Our proposed method effectively increases the classification accuracy in comparison with flat multiple classification methods.
