Noise attenuation in a low-dimensional manifold

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. V321-V334 ◽  
Author(s):  
Siwei Yu ◽  
Stanley Osher ◽  
Jianwei Ma ◽  
Zuoqiang Shi
Keyword(s):  
Seismic Data ◽  
Optimization Problem ◽  
Signal To Noise Ratio ◽  
Dimensional Manifold ◽  
Noise Attenuation ◽  
Noise Levels ◽  
Seismic Wavelet ◽  
Fidelity Term ◽  
Low Dimensional ◽  
Low Dimensional Manifold

We have found that seismic data can be described in a low-dimensional manifold, and then we investigated using a low-dimensional manifold model (LDMM) method for extremely strong noise attenuation. The LDMM supposes the dimension of the patch manifold of seismic data should be low. In other words, the degree of freedom of the patches should be low. Under the linear events assumption on a patch, the patch can be parameterized by the intercept and slope of the event, if the seismic wavelet is identical everywhere. The denoising problem is formed as an optimization problem, including a fidelity term and an LDMM regularization term. We have tested LDMM on synthetic seismic data with different noise levels. LDMM achieves better denoised results in comparison with the Fourier, curvelet and nonlocal mean filtering methods, especially in the presence of strong noise or low signal-to-noise ratio situations. We have also tested LDMM on field records, indicating that LDMM is a method for handling relatively strong noise and preserving weak features.

scholarly journals Low-dimensional manifold of actin polymerization dynamics

2017 ◽  
Vol 19 (12) ◽  
pp. 125012 ◽  
Author(s):  
Carlos Floyd ◽  
Christopher Jarzynski ◽  
Garegin Papoian
Keyword(s):  
Actin Polymerization ◽  
Dimensional Manifold ◽  
Low Dimensional ◽  
Low Dimensional Manifold

scholarly journals Latent learning drives sleep-dependent plasticity in distinct CA1 subpopulations

2020 ◽  
Author(s):  
Wei Guo ◽  
Jie J. Zhang ◽  
Jonathan P. Newman ◽  
Matthew A. Wilson
Keyword(s):  
Hippocampal Neurons ◽  
Dimensional Manifold ◽  
Latent Learning ◽  
Neural Ensembles ◽  
Correlated Activity ◽  
Place Fields ◽  
Internal States ◽  
Low Dimensional ◽  
Low Dimensional Manifold ◽  
The Brain

AbstractLatent learning allows the brain the transform experiences into cognitive maps, a form of implicit memory, without reinforced training. Its mechanism is unclear. We tracked the internal states of the hippocampal neural ensembles and discovered that during latent learning of a spatial map, the state space evolved into a low-dimensional manifold that topologically resembled the physical environment. This process requires repeated experiences and sleep in-between. Further investigations revealed that a subset of hippocampal neurons, instead of rapidly forming place fields in a novel environment, remained weakly tuned but gradually developed correlated activity with other neurons. These ‘weakly spatial’ neurons bond activity of neurons with stronger spatial tuning, linking discrete place fields into a map that supports flexible navigation.

Large-eddy simulation of direct injection natural gas combustion in a heavy-duty truck engine using modified conditional moment closure model with low-dimensional manifold method

2018 ◽  
Vol 21 (5) ◽  
pp. 824-837 ◽  
Author(s):  
Jian Huang ◽  
Gordon McTaggart-Cowan ◽  
Sandeep Munshi
Keyword(s):  
Natural Gas ◽  
Direct Injection ◽  
Moment Closure ◽  
Dimensional Manifold ◽  
Conditional Moment ◽  
Gas Combustion ◽  
Conditional Moment Closure ◽  
Natural Gas Combustion ◽  
Low Dimensional ◽  
Low Dimensional Manifold

This article describes the application of a modified first-order conditional moment closure model used in conjunction with the trajectory-generated low-dimensional manifold method in large-eddy simulation of pilot ignited high-pressure direct injection natural gas combustion in a heavy-duty diesel engine. The article starts with a review of the intrinsic low-dimensional manifold method for reducing detailed chemistry and various formulations for the construction of such manifolds. It is followed by a brief review of the conditional moment closure method for modelling the interaction between turbulence and combustion chemistry. The high computational cost associated with the direct implementation of the basic conditional moment closure model was discussed. The article then describes the formulation of a modified approach to solve the conditional moment closure equation, whose reaction source terms for the conditional mass fractions for species were obtained by projecting the turbulent perturbation onto the reaction manifold. The main model assumptions were explained and the resulting limitations were discussed. A numerical experiment was conducted to examine the validity the model assumptions. The model was then implemented in a combustion computational fluid dynamics solver developed on an open-source computational fluid dynamics platform. Non-reactive jet simulations were first conducted and the results were compared to the experimental measurement from a high-pressure visualization chamber to verify that the jet penetration under engine relevant conditions was correctly predicted. The model was then used to simulate natural gas combustion in a heavy-duty diesel engine equipped with a high-pressure direct injection system. The simulation results were compared with the experimental measurement from a research engine to verify the accuracy of the model for both the combustion rate and engine-out emissions.

W-LDMM: A Wasserstein driven low-dimensional manifold model for noisy image restoration

2020 ◽  
Vol 371 ◽  
pp. 108-123 ◽  
Author(s):  
Ruiqiang He ◽  
Xiangchu Feng ◽  
Weiwei Wang ◽  
Xiaolong Zhu ◽  
Chunyu Yang
Keyword(s):  
Image Restoration ◽  
Dimensional Manifold ◽  
Noisy Image ◽  
Low Dimensional ◽  
Low Dimensional Manifold

Random noise attenuation by planar mathematical morphological filtering

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. V11-V25 ◽  
Author(s):  
Weilin Huang ◽  
Runqiu Wang
Keyword(s):  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Seismic Exploration ◽  
Noise Attenuation ◽  
Seismic Waveforms ◽  
Morphological Filtering ◽  
Alternative Techniques ◽  
The Difference ◽  
The Relationship

Improving the signal-to-noise ratio (S/N) of seismic data is desirable in many seismic exploration areas. The attenuation of random noise can help to improve the S/N. Geophysicists usually use the differences between signal and random noise in certain attributes, such as frequency, wavenumber, or correlation, to suppress random noise. However, in some cases, these differences are too small to be distinguished. We used the difference in planar morphological scales between signal and random noise to separate them. The planar morphological scale is the information that describes the regional shape of seismic waveforms. The attenuation of random noise is achieved by removing the energy in the smaller morphological scales. We call our method planar mathematical morphological filtering (PMMF). We analyze the relationship between the performance of PMMF and its input parameters in detail. Applications of the PMMF method to synthetic and field post/prestack seismic data demonstrate good performance compared with competing alternative techniques.

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