Sangjun Han, profile picture
Uploaded bySangjun Han
222 views

Feasibility of EEG Super-Resolution Using Deep Convolutional Networks

This document summarizes a master's thesis presentation on using deep convolutional networks for EEG spatial super-resolution. The study used simulated EEG data to test how different noise types and upscaling ratios affect the super-resolution process. Key findings include that super-resolution recovered low-resolution signals beyond the level of high-resolution signals for white noise, but only to the level of high-resolution signals for real noise. Higher upscaling ratios yielded better quality signals for white noise. Whitening real noise helped super-resolution, especially for source analysis at low SNR. The study used simulations to isolate the effects of noise types since real EEG noise sources cannot be extracted.

Embed presentation

Download to read offline
A Simulation Study of EEG Spatial Super-Resolution Using Deep Convolutional Networks 2018. 05. 30 Sangjun Han Gwangju Institute of Science and Technology School of Electrical Engineering and Computer Science BioComputing Lab, Prof. Sung Chan Jun Presentation for Master’s Thesis
• Introduction - Electroencephalography - Deep Learning - Related Work - Motivation • Method - Data Generation - Source Localization - Data Preparation - Deep Convolutional Networks - Evaluation Metrics • Results - Result 1 – Conclusion 1 - Result 2 – Conclusion 2 - Result 3 – Conclusion 3 • Discussion • Summary • Publication • References Index 2
Introduction 3
Electroencephalography • Electroencephalography (EEG) - Measures electrical potential of brain on the scalp - Temporal and spatial dynamics - Non-invasively measured - Is mixed signal originated from brain sources EEG systems Sensor and source level source sensor 4
Electroencephalography • Improving spatial resolution of EEG - High-density EEG hardware can be used, but it requires a lot of cost 32 channels 64 channels 128 channels 256 channels Experimental cost↑ • Resolution of EEG - High temporal resolution - But relatively low spatial resolution 5
Electroencephalography • Low spatial resolution EEG... - May cause aliasing in spatial frequency [1] Topological difference between 16 channels and 64 channels EEG 64 channels16 channels 6
Electroencephalography • Low spatial resolution EEG... - Increasing the electrode number helps decrease localization error [2] Mean source localization error for 5 subjects 7
Deep Learning • The success of deep learning ... - Backpropagation appeared (1986) [3] - Weight initialization by restricted Boltzmann machine (2010) [4] - High accuracy in speech recognition (2012) [5] - High accuracy in image classification (2012) [6] - Image localization, detection, segmentation, ... super-resolution! Super-resolution (SR) Recovering a high-resolution image from a single low-resolution image • Image super-resolution 8
• Image super-resolution SRCNN, Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] Related Work 9
• Image super-resolution SRCNN, Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] How to optimize effectively and efficiently by reconstructing networks’ structure Related Work 10
• Image super-resolution SRCNN, Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] To satisfy human’s visual perception with a new concept of loss function Related Work 11
• Image super-resolution High-resolution (HR) Original image Related Work 12
• Image super-resolution High-resolution (HR) Blurring, Sub-sampling Original image Low-resolution (LR) Related Work 13
• Image super-resolution High-resolution (HR) Train neural networks min θ ( 𝐻𝑅 − 𝐿𝑅)2 Original image Low-resolution (LR) Related Work 14
• Image super-resolution High-resolution (HR) Original image Low-resolution (LR) Trained model Super-resolution (SR) Recovered image Related Work 15
• Audio super-resolution - V. Kuleshov, 2017 [11] - Regarded as generative model - Temporally up-scaled - Bandwidth extension, thus predicting higher frequencies Related Work 16
• EEG super-resolution - I. A. Corley, 2018 [12] - Mental imagery open dataset, 3 classes - Spatially up-scaled, 16 to 32 channels (2x), 8 to 32 channels (4x) - Evaluated SR performance by classification results Related Work 17
Motivation • Enhancing spatial resolution of EEG using deep learning - Not merely interpolating a few missing channels - Rather, scaling up the number of channels to several folds - We can acquire high quality data without high experimental cost - Observing properties of super-resolved EEG at sensor and source level Super-resolution (SR) • Limitation of previous work - How about properties of super-resolved EEG signal? 18
Motivation • Questions 1. How does noise type affect the EEG SR process? 2. How does SR deep learning work over various upscaling sizes? (2x, 4x, 8x) 3. Are there any approaches to improve signal quality during SR process? Sensor and source level source sensor white Gaussian noise real environmental noise 19
Method 20
Data Generation • Head model and channel information - 3-shell spherical boundary element method (BEM) - HydroCel GSN systems (Electrical Geodescis. Inc.) 1 0.92 0.87 Brain σ : 1 Skull σ : 0.0125 Scalp σ : 1 spherical head model GSN 128 layout 21
Data Generation noiseless scalp EEG • Noiseless scalp EEG - Two dipoles were projected on scalp EEG sensors - Sampled at 250 Hz, and one trial lasted for 1 second two dipoles (blue dots) 22
Data Generation + Simulation EEG noiseless scalp EEG white Gaussian noise real noise or • Adding noise to scalp EEG - Adding white Gaussian noise and real noise - Real noise was measured from one subject resting state - Adjusting SNR 10, 5, 1, 0.5, 0.1, 0.05, and 0.01 two dipoles (blue dots) 23
Source Localization + Simulation EEG noiseless scalp EEG white Gaussian noise real noise or two dipoles (blue dots) • Source Localization - Array-gain minimum variance beamformer [13] - Beamforming scanned at a 7 mm scanning interval - On 10,000 voxels 24
Data Preparation ex) For 16 to 128 channels HR (128 channels) 0 200 400 600 800 1000 25
Data Preparation ex) For super-resolution from 16 to 128 channels HR (128 channels)LR (16 channels) select 16 channels 0 200 400 600 800 10000 200 400 600 800 1000 26
Data Preparation HR (128 channels)LR (16 channels) select 16 channels interpolated with the average of its neighbor LR (128 channels) ex) For super-resolution from 16 to 128 channels 0 200 400 600 800 10000 200 400 600 800 1000 0 200 400 600 800 1000 27
Data Preparation HR (128 channels)LR (16 channels) select 16 channels interpolated with the average of its neighbor LR (128 channels) train neural networks min θ ( 𝐻𝑅 − 𝐿𝑅)2 - This is an ill-posed problem - For good starting initialization [7] 16 to 32 (2x) 16 to 64 (4x) 16 to 128 (8x) ex) For super-resolution from 16 to 128 channels 0 200 400 600 800 10000 200 400 600 800 1000 0 200 400 600 800 1000 28
Deep Convolutional Networks LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13 X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 • Settings - Convolution for down-sampling - Transposed convolution for up-sampling - Adam optimizer (first-order gradient optimization) [14] - He initializer [15] - Linear activation function (y = x) was used 29
Deep Convolutional Networks • Dataset - Training for 1,600 trials - Testing for 400 trials * 50 times = 20,000 trials - Averaging testing results for statistical stability LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13 X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 30
Evaluation Metrics • Evaluation metrics - Mean squared error (MSE, at sensor level) - Correlation (at sensor level) - Error distance between dipole locations (at source level) SLR SHR SSRvs. vs. Noiseless Scalp EEG SLR : Low-resolution signal, SHR : High-resolution signal, SSR : Super-resolved signal 31 MSE Correlation Error distance MSE Correlation Error distance MSE Correlation Error distance
Evaluation Metrics • Evaluation metrics - Mean squared error (MSE, at sensor level) - Correlation (at sensor level) - Error distance between dipole locations (at source level) Mean Euclidean distance between voxels that activate over arbitrary power thresholds and original dipoles 32
Results 1 How does noise type affect the EEG SR process? 33
Result 1 White Gaussian Noise • According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, MSE increases - For all SNR, SR case has minimum loss 34
• According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, correlation decreases - For all SNR, SR case has maximum correlation Result 1 White Gaussian Noise 35
• According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, error distance increases - For most of SNR, SR case has minimum error distance Result 1 White Gaussian Noise 36
• According to SNR (when 16 to 64) The time series of one trial at E01 channel, when SNR 0.5 - The SSR catches well the shape of noiseless scalp EEG 0 200 400 600 800 1000 Result 1 White Gaussian Noise 37
Source localization results, when SNR 0.5 HR SR LR Result 1 White Gaussian Noise 38Source localization results, when SNR 0.5
Source localization results, when SNR 0.5 Result 1 White Gaussian Noise 39Source localization results, when SNR 0.5 The SR case detects dipole position well HR SR LR
• According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, MSE increases - For all SNR, SR case has similar loss with HR case Result 1 Real Noise 40
• According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, correlation decreases - For most of SNR, SR case has similar correlation with HR case Result 1 Real Noise 41
• According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, error distance increases - Except for very low SNR, SR case has similar error distance with HR case Result 1 Real Noise 42
• According to SNR (when 16 to 64) The time series of one trial at E01 channel, when SNR 0.5 - It is hard to find general shape of SSR - But the SSR follows tendency of SHR 0 200 400 600 800 1000 Result 1 Real Noise 43
Source localization results, when SNR 0.5 Result 1 Real Noise 44 HR SR LR
Conclusion 1 • The case of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) 45
Results 2 How does SR deep learning work over various up-scaling sizes? 46
• According to upscaling ratio (when SNR 0.5) - When upscaling ratio increases, MSE decreases - For all upscaling ratio, SR case has minimum loss Result 2 White Gaussian Noise 47
• According to upscaling ratio (when SNR 0.5) - When upscaling ratio increases, correlation increases - For all upscaling ratio, SR has maximum correlation Result 2 White Gaussian Noise 48
• According to upscaling ratio (when SNR 0.5) - At upscaling ratio is set to 16 to 128, error distance is minimum - For all upscaling ratio, SR case has minimum error distance Result 2 White Gaussian Noise 49
• According to upscaling ratio (when SNR 0.5) - SR reproduced the signal from SSR to the level of SHR Result 2 Real Noise 50
Conclusion 2 • The case of white Gaussian noise - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - There was no significant difference over various upscaling ratio 51
Conclusion 1 + 2 • The case of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) - There was no significant difference over various upscaling ratio 52
Conclusion 1 + 2 • The case of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) - There was no significant difference over various upscaling ratio Whitening! 53
Results 3 Are there any approaches to improve signal quality during SR? 54
C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise) Result 3 Whitening Real Noise 55
• According to SNR (when 16 to 64) - For all SNR, whitened SR case is a little nosier than just SR case Result 3 Whitening Real Noise 56 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
• According to SNR (when 16 to 64) - For most of SNR, whitened SR case is less correlated than SR case Result 3 Whitening Real Noise 57 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
• According to SNR (when 16 to 64) - At very low SNR, error distance from whitened SR is reduced Result 3 Whitening Real Noise 58 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
Source localization results, when SNR 0.5 Result 3 Whitening Real Noise 59 SR Whitened SR
Conclusion 3 • Whitening of real noise - can be effective for SR - especially for source analysis 60
Discussion 61
Discussion 1 • Why simulation study? - In real EEG, it is difficult to extract only brain signal from its noise - Because of its noise, we don’t know exact dipole locations - We can’t observe the influence of noise type Exact dipole location from simulation data 62
Discussion 2 white Gaussian noise real noise • On same SNR - The case of white Gaussian noise seems to be noisier than real noise one - Eye component in the real noise occupied the noise’s overall power - It is difficult to make an equivalent comparison between them 63
Discussion 3 • Why does SR work well at 16 to 128? - Although it is the case of only white Gaussian noise - We can interpret it as the properties of data-driven approach 64
Discussion 3 - Higher-dimensional answer provides us with more fruitful information - But in real noise case, it may not be useful information LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13 X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 16 32 64 128 • Our experimental design 65
Discussion 4 • Why did we choose a linear function for deep learning? - It is typical to use non-linear functions to extract features hyperbolic tangent function (tanh) rectified linear unit (ReLU) -1 ≤ y ≤ 1 0 ≤ y ≤ ∞ 66
Discussion 4 • Why did we choose a linear function for deep learning? - Let’s regard our problem as finding optimal fitted line min θ ( 𝐻𝑅 − 𝐿𝑅)2 67
Discussion 4 • Why did we choose a linear function for deep learning? - Let’s regard our problem as finding optimal fitted line min θ ( 𝐻𝑅 − 𝐿𝑅)2 68
Summary 69 • Deep learning based SR may be effective on EEG - EEG SR can reduce experimental cost significantly - EEG SR can provide high resolution data without much effort
Summary 70 • Deep learning based SR may be effective on EEG - At sensor and source level - During SR, ideal noise can be canceled out => improve signal quality - In real noisy environment, EEG may be acceptably super-resolved - If we know more sensor information, it may be useful for SR - Whitening could be effective for SR • Limitations - However, it has limitation of data-driven approach => need HR data - We need to conduct more experiments on real EEG data
Publication • EEG super-resolution [1] Sangjun Han, Moonyoung Kwon, Sung Chan Jun, “Feasibility Study of EEG Super-Resolution Using Deep Convolutional Networks,” IEEE International Conference on Systems, Man, and Cybernetics, Oct 2018 (Submitted) [2] Sangjun Han, Moonyoung Kwon, Sunghan Lee, Sung Chan Jun, “EEG Spatial Super-Resolution Using Deep Convolutional Linear Networks : a Simulation Study,” Korean Society of Medical & Biological Engineering, Nov 2017 (Best Paper) • EEG emotion classification using deep learning [3] Sunghan Lee, Sangjun Han, Sung Chan Jun, “EEG-based Classification of Multi-class Emotional States Using One- dimensional Convolutional Neural Networks,” 7th Graz BCI Conference, July 2017 [4] Sunghan Lee, Sangjun Han, Sung Chan Jun, “Four-Class Emotion Classification Using One-dimensional Convolutional Neural Networks - An EEG Study,” Society for Neuroscience, Nov 2017 • Improving sleep quality by acoustic stimulation [5] Jinyoung Choi, Sangjun Han, Moonyoung Kwon, Hyeon Seo, Sehyeon Jang, Sung Chan Jun, “Study on Subject-Specific Parameters in Sleep Spindle Detection Algorithm,” The IEEE Engineering in Medicine and Biology Conference, July 2017 [6] Jinyoung Choi, Sangjun Han, Kyungho Won, Sung Chan Jun, “Effect of Acoustic Stimulation after Sleep Spindle Activity,” Sleep Medicine, Oct 2017 [7] Jinyoung Choi, Sangjun Han, Kyungho Won, Sung Chan Jun, “The Neurophysiological Effect of Acoustic Stimulation with Real-time Sleep Spindle Detection,” The IEEE Engineering in Medicine and Biology Conference, July 2018 Refereed Conference Paper 71
References [1] D. M. Tucker, “Spatial Sampling of Head Electrical Fields: The Geodesic Sensor Net,” Electroencephalography and Clinical Neurophysiology, vol. 87, pp. 154–163, September 1993. [2] A. Sohrabpour, Y. Lu, P. Kankirawatana, J. Blount, H. Kim, and B. He, “Effect of EEG Electrode Number on Epileptic Source Localization in Pediatric Patients,” Clinical Neurophysiology, vol. 126, pp. 472-480, December 2015. [3] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning Representations by Back-propagating errors,” Nature, vol. 323, pp. 533-536, October 1986. [4] G. E. Hinton, “A Practical Guide to Training Restricted Boltzmann Machines,” Lecture Notes in Department of Computer Science, University of Toronto, August 2010. [5] D. George, Y. Dong, D. Li and A. Alex, “Context-Dependent Pre-Trained Deep Neural Networks for Large- Vocabulary Speech Recognition,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 20, no. 1, pp. 30- 42, January 2012. [6] K. Alex, S. Ilya and H. Geoffrey, “ImageNet Classification with Deep Convolutional Neural Networks,” in Proceedings of the Neural Information Processing Systems, December 2012. [7] C. Dong, C. C. Loy, and X. Tang, “Image Super-Resolution Using Deep Convolutional Networks,” IEEE Transactions on Pattern Analysis and Machie Intelligence, vol. 38, pp. 295–307, June 2015. [8] J. Kim, J. K. Lee, and L. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” Conference on Computer Vision and Pattern Recognition, pp. 1637–1645, June 2016. [9] W. Shi, J. Caballero, F. Huszar, J. Totz, A. P. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” Conference on Computer Vision and Pattern Recognition, pp. 1874–1883, June 2016. [10] C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, amd W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” Conference on Computer Vision and Pattern Recognition, pp. 4681–4690, July 2017. [11] V. Kuleshov, S. Z. Enam, and S. Ermon, “Audio Super-Resolution Using Neural Nets,” Workshop of International Conference on Learning Representation, April 2017. [12] I. A. Corley, and Y. Huang, “Deep EEG Super-Resolution: Upsampling EEG Spatial Resolution with Generative Adversarial Networks,” IEEE EMBS International Conference on Biomedical & Health Informatics, March 2018 [13] K. Sekihara, and S. S. Nagarajan, Adaptive Spatial Filters for Electromagnetic Brain Imaging, 1st ed., Springer-Verlag Berlin Heidelberg, 2008. [14] P. Kingma, and J. Ba, “ADAM: A Method for Stochastic Optimization,” International Conference on Learning Representation, arXiv:1412.6980, May 2015. [15] K. He, X, Zhang, S. Ren, and J. Sun, “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,” International Conference on Computer Vision, pp. 1026–1034, December 2015. 72
Thank you 73

More Related Content

PPTX
EEG Signal processing
byDikshaKalra9
 
PDF
Real Time Implementation of Active Noise Control
byChittaranjan Baliarsingh
 
PDF
Robust Video Denoising and Singing-Voice Separation using Low-rank matrix com...
byAyush Singh, MS
 
PPTX
An Introduction to Electroencephalography
byJoshua Baker
 
PDF
E44082429
byIJERA Editor
 
PPTX
FrB18_2_Krishnamoorthy_Venkatasubramanian.pptx
byVenkatasubramanianKr8
 
PPTX
ECG DENOISING USING NN.pp
bybobbydm
 
PPTX
Dsp review
byChetanShahukari
 
EEG Signal processing
byDikshaKalra9
 
Real Time Implementation of Active Noise Control
byChittaranjan Baliarsingh
 
Robust Video Denoising and Singing-Voice Separation using Low-rank matrix com...
byAyush Singh, MS
 
An Introduction to Electroencephalography
byJoshua Baker
 
E44082429
byIJERA Editor
 
FrB18_2_Krishnamoorthy_Venkatasubramanian.pptx
byVenkatasubramanianKr8
 
ECG DENOISING USING NN.pp
bybobbydm
 
Dsp review
byChetanShahukari
 

Similar to Feasibility of EEG Super-Resolution Using Deep Convolutional Networks

PDF
EEG Signal Classification using Deep Neural Network
byIRJET Journal
 
PDF
forney_techrep2015
byElliott Forney
 
PDF
An introduction to super resolution using deep learning
byAnil Chandra Naidu Matcha
 
PPTX
Matthew Gray Summer 2015 Presentation
byMatthew Gray
 
PDF
A new approach for Reducing Noise in ECG signal employing Gradient Descent Me...
bypaperpublications3
 
PDF
Gene's law
byHoopeer Hoopeer
 
PDF
Classification of electroencephalography using cooperative learning based on...
byIJECEIAES
 
PPTX
Application of eeg wave
byRohit vijay
 
PDF
ct_meeting_final_jcy (1).pdf
byssuser2c7393
 
PDF
[Research] Detection of MCI using EEG Relative Power + DNN
byDonghyeon Kim
 
PDF
IJCER (www.ijceronline.com) International Journal of computational Engineerin...
byijceronline
 
PPTX
Eva Mohedano, "Investigating EEG for Saliency and Segmentation Applications i...
byUniversitat Politècnica de Catalunya
 
PPTX
EEG Basics monish.pptx
byMohinishS
 
PPTX
Introduction to deep Learning Fundamentals
byVishalGour25
 
PDF
Signal Processing for Neuroscientists 1st Edition Wim Van Drongelen All Chapt...
bybouhetzuhod
 
PDF
A Review on ECG -Signal Classification of Scalogram Snap shots the use of Con...
byIRJET Journal
 
PDF
Super resolution in deep learning era - Jaejun Yoo
byJaeJun Yoo
 
PDF
IRJET- Classification of Arrhythmic ECG Data using Artificial Neural Network
byIRJET Journal
 
PPT
Sleep 2008 Electronicsv.3
byweckhardt
 
PPTX
Biomedical Signals Classification With Transformer Based Model.pptx
bySandeep Kumar
 
EEG Signal Classification using Deep Neural Network
byIRJET Journal
 
forney_techrep2015
byElliott Forney
 
An introduction to super resolution using deep learning
byAnil Chandra Naidu Matcha
 
Matthew Gray Summer 2015 Presentation
byMatthew Gray
 
A new approach for Reducing Noise in ECG signal employing Gradient Descent Me...
bypaperpublications3
 
Gene's law
byHoopeer Hoopeer
 
Classification of electroencephalography using cooperative learning based on...
byIJECEIAES
 
Application of eeg wave
byRohit vijay
 
ct_meeting_final_jcy (1).pdf
byssuser2c7393
 
[Research] Detection of MCI using EEG Relative Power + DNN
byDonghyeon Kim
 
IJCER (www.ijceronline.com) International Journal of computational Engineerin...
byijceronline
 
Eva Mohedano, "Investigating EEG for Saliency and Segmentation Applications i...
byUniversitat Politècnica de Catalunya
 
EEG Basics monish.pptx
byMohinishS
 
Introduction to deep Learning Fundamentals
byVishalGour25
 
Signal Processing for Neuroscientists 1st Edition Wim Van Drongelen All Chapt...
bybouhetzuhod
 
A Review on ECG -Signal Classification of Scalogram Snap shots the use of Con...
byIRJET Journal
 
Super resolution in deep learning era - Jaejun Yoo
byJaeJun Yoo
 
IRJET- Classification of Arrhythmic ECG Data using Artificial Neural Network
byIRJET Journal
 
Sleep 2008 Electronicsv.3
byweckhardt
 
Biomedical Signals Classification With Transformer Based Model.pptx
bySandeep Kumar
 

Recently uploaded

PDF
Startup Formation Collapses While Acquisition Activity Hits New High!
byMemoori
 
PDF
Configure and Manage Systemd Timers- RHCSA (RH134).pdf
byLinuxCert Guru
 
PDF
Making Search Less Taxing: Leveraging Semantics and Keywords in Hybrid Search
byEnterprise Knowledge
 
PDF
Rustici Software: eLearning standards in the age of AI
byRustici Software
 
PDF
The Emergence of Empathic XR: AWE Asia 2026 keynote
byMark Billinghurst
 
PPTX
Retrieval Augmented Generation- The Synergistic Power of Prompt Engineering
bySemantic SEO BD
 
PDF
Python Automation in Action: Real-World Use Cases and Practical Implementation
byDenys Smirnov
 
PDF
GenerationAI Paris 2025 | How Agentic AI is Reinventing Organizations
byapidays
 
PDF
UiPath Automation Developer Associate Training Series 2026 - Session 2
byDianaGray10
 
PDF
final.pdf
byomarbishtawi04
 
PPTX
How Does an ICO Launchpad Work Step-by-Step Breakdown.pptx
byTom Hardy S
 
PDF
Explaining specific examples of purpose-specific BOM
byakipii ogaoga
 
PPTX
Celonis Optimizing your future with process
bydevjeremyappleyard
 
PDF
Post Quantum Cryptography for Dummies.pdf
byAde Ismail Isnan
 
PDF
Self-Correction Failure Diagnostic: Detecting Drift in Complex Systems
bySystems Research Group
 
PDF
Mount File Systems using UUID and Label - RHCSA (RH134).pdf
byLinuxCert Guru
 
PDF
Poročilo odbora CIS (CH08873) za leto 2025 na letni skupščini IEEE Slovenija ...
byUniversity of Maribor
 
PDF
How does MES(Manufacturing Execution System) work?
byakipii ogaoga
 
PDF
Safer’s Picks: The 5 FME Transformers You Didn’t Know You Needed
bySafe Software
 
PDF
From DeFi POC to Production MVP - A 12-16 Week Blueprint.pdf
byniahiggins21
 
Startup Formation Collapses While Acquisition Activity Hits New High!
byMemoori
 
Configure and Manage Systemd Timers- RHCSA (RH134).pdf
byLinuxCert Guru
 
Making Search Less Taxing: Leveraging Semantics and Keywords in Hybrid Search
byEnterprise Knowledge
 
Rustici Software: eLearning standards in the age of AI
byRustici Software
 
The Emergence of Empathic XR: AWE Asia 2026 keynote
byMark Billinghurst
 
Retrieval Augmented Generation- The Synergistic Power of Prompt Engineering
bySemantic SEO BD
 
Python Automation in Action: Real-World Use Cases and Practical Implementation
byDenys Smirnov
 
GenerationAI Paris 2025 | How Agentic AI is Reinventing Organizations
byapidays
 
UiPath Automation Developer Associate Training Series 2026 - Session 2
byDianaGray10
 
final.pdf
byomarbishtawi04
 
How Does an ICO Launchpad Work Step-by-Step Breakdown.pptx
byTom Hardy S
 
Explaining specific examples of purpose-specific BOM
byakipii ogaoga
 
Celonis Optimizing your future with process
bydevjeremyappleyard
 
Post Quantum Cryptography for Dummies.pdf
byAde Ismail Isnan
 
Self-Correction Failure Diagnostic: Detecting Drift in Complex Systems
bySystems Research Group
 
Mount File Systems using UUID and Label - RHCSA (RH134).pdf
byLinuxCert Guru
 
Poročilo odbora CIS (CH08873) za leto 2025 na letni skupščini IEEE Slovenija ...
byUniversity of Maribor
 
How does MES(Manufacturing Execution System) work?
byakipii ogaoga
 
Safer’s Picks: The 5 FME Transformers You Didn’t Know You Needed
bySafe Software
 
From DeFi POC to Production MVP - A 12-16 Week Blueprint.pdf
byniahiggins21
 

Feasibility of EEG Super-Resolution Using Deep Convolutional Networks

  • 1.
    A Simulation Studyof EEG Spatial Super-Resolution Using Deep Convolutional Networks 2018. 05. 30 Sangjun Han Gwangju Institute of Science and Technology School of Electrical Engineering and Computer Science BioComputing Lab, Prof. Sung Chan Jun Presentation for Master’s Thesis
  • 2.
    • Introduction - Electroencephalography -Deep Learning - Related Work - Motivation • Method - Data Generation - Source Localization - Data Preparation - Deep Convolutional Networks - Evaluation Metrics • Results - Result 1 – Conclusion 1 - Result 2 – Conclusion 2 - Result 3 – Conclusion 3 • Discussion • Summary • Publication • References Index 2
  • 3.
  • 4.
    Electroencephalography • Electroencephalography (EEG) -Measures electrical potential of brain on the scalp - Temporal and spatial dynamics - Non-invasively measured - Is mixed signal originated from brain sources EEG systems Sensor and source level source sensor 4
  • 5.
    Electroencephalography • Improving spatialresolution of EEG - High-density EEG hardware can be used, but it requires a lot of cost 32 channels 64 channels 128 channels 256 channels Experimental cost↑ • Resolution of EEG - High temporal resolution - But relatively low spatial resolution 5
  • 6.
    Electroencephalography • Low spatialresolution EEG... - May cause aliasing in spatial frequency [1] Topological difference between 16 channels and 64 channels EEG 64 channels16 channels 6
  • 7.
    Electroencephalography • Low spatialresolution EEG... - Increasing the electrode number helps decrease localization error [2] Mean source localization error for 5 subjects 7
  • 8.
    Deep Learning • Thesuccess of deep learning ... - Backpropagation appeared (1986) [3] - Weight initialization by restricted Boltzmann machine (2010) [4] - High accuracy in speech recognition (2012) [5] - High accuracy in image classification (2012) [6] - Image localization, detection, segmentation, ... super-resolution! Super-resolution (SR) Recovering a high-resolution image from a single low-resolution image • Image super-resolution 8
  • 9.
    • Image super-resolution SRCNN,Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] Related Work 9
  • 10.
    • Image super-resolution SRCNN,Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] How to optimize effectively and efficiently by reconstructing networks’ structure Related Work 10
  • 11.
    • Image super-resolution SRCNN,Dong et al. 2015 [7] DRCN, Kim et al. 2015 [8] ESPCN, Shi et al. 2016 [9] SRGAN, Ledig et al. 2016 [10] To satisfy human’s visual perception with a new concept of loss function Related Work 11
  • 12.
    • Image super-resolution High-resolution(HR) Original image Related Work 12
  • 13.
    • Image super-resolution High-resolution(HR) Blurring, Sub-sampling Original image Low-resolution (LR) Related Work 13
  • 14.
    • Image super-resolution High-resolution(HR) Train neural networks min θ ( 𝐻𝑅 − 𝐿𝑅)2 Original image Low-resolution (LR) Related Work 14
  • 15.
    • Image super-resolution High-resolution(HR) Original image Low-resolution (LR) Trained model Super-resolution (SR) Recovered image Related Work 15
  • 16.
    • Audio super-resolution -V. Kuleshov, 2017 [11] - Regarded as generative model - Temporally up-scaled - Bandwidth extension, thus predicting higher frequencies Related Work 16
  • 17.
    • EEG super-resolution -I. A. Corley, 2018 [12] - Mental imagery open dataset, 3 classes - Spatially up-scaled, 16 to 32 channels (2x), 8 to 32 channels (4x) - Evaluated SR performance by classification results Related Work 17
  • 18.
    Motivation • Enhancing spatialresolution of EEG using deep learning - Not merely interpolating a few missing channels - Rather, scaling up the number of channels to several folds - We can acquire high quality data without high experimental cost - Observing properties of super-resolved EEG at sensor and source level Super-resolution (SR) • Limitation of previous work - How about properties of super-resolved EEG signal? 18
  • 19.
    Motivation • Questions 1. Howdoes noise type affect the EEG SR process? 2. How does SR deep learning work over various upscaling sizes? (2x, 4x, 8x) 3. Are there any approaches to improve signal quality during SR process? Sensor and source level source sensor white Gaussian noise real environmental noise 19
  • 20.
  • 21.
    Data Generation • Headmodel and channel information - 3-shell spherical boundary element method (BEM) - HydroCel GSN systems (Electrical Geodescis. Inc.) 1 0.92 0.87 Brain σ : 1 Skull σ : 0.0125 Scalp σ : 1 spherical head model GSN 128 layout 21
  • 22.
    Data Generation noiseless scalpEEG • Noiseless scalp EEG - Two dipoles were projected on scalp EEG sensors - Sampled at 250 Hz, and one trial lasted for 1 second two dipoles (blue dots) 22
  • 23.
    Data Generation + SimulationEEG noiseless scalp EEG white Gaussian noise real noise or • Adding noise to scalp EEG - Adding white Gaussian noise and real noise - Real noise was measured from one subject resting state - Adjusting SNR 10, 5, 1, 0.5, 0.1, 0.05, and 0.01 two dipoles (blue dots) 23
  • 24.
    Source Localization + SimulationEEG noiseless scalp EEG white Gaussian noise real noise or two dipoles (blue dots) • Source Localization - Array-gain minimum variance beamformer [13] - Beamforming scanned at a 7 mm scanning interval - On 10,000 voxels 24
  • 25.
    Data Preparation ex) For16 to 128 channels HR (128 channels) 0 200 400 600 800 1000 25
  • 26.
    Data Preparation ex) Forsuper-resolution from 16 to 128 channels HR (128 channels)LR (16 channels) select 16 channels 0 200 400 600 800 10000 200 400 600 800 1000 26
  • 27.
    Data Preparation HR (128channels)LR (16 channels) select 16 channels interpolated with the average of its neighbor LR (128 channels) ex) For super-resolution from 16 to 128 channels 0 200 400 600 800 10000 200 400 600 800 1000 0 200 400 600 800 1000 27
  • 28.
    Data Preparation HR (128channels)LR (16 channels) select 16 channels interpolated with the average of its neighbor LR (128 channels) train neural networks min θ ( 𝐻𝑅 − 𝐿𝑅)2 - This is an ill-posed problem - For good starting initialization [7] 16 to 32 (2x) 16 to 64 (4x) 16 to 128 (8x) ex) For super-resolution from 16 to 128 channels 0 200 400 600 800 10000 200 400 600 800 1000 0 200 400 600 800 1000 28
  • 29.
    Deep Convolutional Networks LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 • Settings - Convolution for down-sampling - Transposed convolution for up-sampling - Adam optimizer (first-order gradient optimization) [14] - He initializer [15] - Linear activation function (y = x) was used 29
  • 30.
    Deep Convolutional Networks •Dataset - Training for 1,600 trials - Testing for 400 trials * 50 times = 20,000 trials - Averaging testing results for statistical stability LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13 X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 30
  • 31.
    Evaluation Metrics • Evaluationmetrics - Mean squared error (MSE, at sensor level) - Correlation (at sensor level) - Error distance between dipole locations (at source level) SLR SHR SSRvs. vs. Noiseless Scalp EEG SLR : Low-resolution signal, SHR : High-resolution signal, SSR : Super-resolved signal 31 MSE Correlation Error distance MSE Correlation Error distance MSE Correlation Error distance
  • 32.
    Evaluation Metrics • Evaluationmetrics - Mean squared error (MSE, at sensor level) - Correlation (at sensor level) - Error distance between dipole locations (at source level) Mean Euclidean distance between voxels that activate over arbitrary power thresholds and original dipoles 32
  • 33.
    Results 1 How doesnoise type affect the EEG SR process? 33
  • 34.
    Result 1 WhiteGaussian Noise • According to SNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, MSE increases - For all SNR, SR case has minimum loss 34
  • 35.
    • According toSNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, correlation decreases - For all SNR, SR case has maximum correlation Result 1 White Gaussian Noise 35
  • 36.
    • According toSNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, error distance increases - For most of SNR, SR case has minimum error distance Result 1 White Gaussian Noise 36
  • 37.
    • According toSNR (when 16 to 64) The time series of one trial at E01 channel, when SNR 0.5 - The SSR catches well the shape of noiseless scalp EEG 0 200 400 600 800 1000 Result 1 White Gaussian Noise 37
  • 38.
    Source localization results,when SNR 0.5 HR SR LR Result 1 White Gaussian Noise 38Source localization results, when SNR 0.5
  • 39.
    Source localization results,when SNR 0.5 Result 1 White Gaussian Noise 39Source localization results, when SNR 0.5 The SR case detects dipole position well HR SR LR
  • 40.
    • According toSNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, MSE increases - For all SNR, SR case has similar loss with HR case Result 1 Real Noise 40
  • 41.
    • According toSNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, correlation decreases - For most of SNR, SR case has similar correlation with HR case Result 1 Real Noise 41
  • 42.
    • According toSNR (when 16 to 64) - For each LR, HR, and SR case, when SNR decreases, error distance increases - Except for very low SNR, SR case has similar error distance with HR case Result 1 Real Noise 42
  • 43.
    • According toSNR (when 16 to 64) The time series of one trial at E01 channel, when SNR 0.5 - It is hard to find general shape of SSR - But the SSR follows tendency of SHR 0 200 400 600 800 1000 Result 1 Real Noise 43
  • 44.
    Source localization results,when SNR 0.5 Result 1 Real Noise 44 HR SR LR
  • 45.
    Conclusion 1 • Thecase of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) 45
  • 46.
    Results 2 How doesSR deep learning work over various up-scaling sizes? 46
  • 47.
    • According toupscaling ratio (when SNR 0.5) - When upscaling ratio increases, MSE decreases - For all upscaling ratio, SR case has minimum loss Result 2 White Gaussian Noise 47
  • 48.
    • According toupscaling ratio (when SNR 0.5) - When upscaling ratio increases, correlation increases - For all upscaling ratio, SR has maximum correlation Result 2 White Gaussian Noise 48
  • 49.
    • According toupscaling ratio (when SNR 0.5) - At upscaling ratio is set to 16 to 128, error distance is minimum - For all upscaling ratio, SR case has minimum error distance Result 2 White Gaussian Noise 49
  • 50.
    • According toupscaling ratio (when SNR 0.5) - SR reproduced the signal from SSR to the level of SHR Result 2 Real Noise 50
  • 51.
    Conclusion 2 • Thecase of white Gaussian noise - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - There was no significant difference over various upscaling ratio 51
  • 52.
    Conclusion 1 +2 • The case of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) - There was no significant difference over various upscaling ratio 52
  • 53.
    Conclusion 1 +2 • The case of white Gaussian noise - SR recovered SLR beyond the level of SHR (both at sensor and source) - At higher upscaling ratio, SR can recover signal of better quality (at sensor, but not convinced at source) • The case of real noise - SR recovered SLR to the level of SHR (at sensor, but not convinced at source) - There was no significant difference over various upscaling ratio Whitening! 53
  • 54.
    Results 3 Are thereany approaches to improve signal quality during SR? 54
  • 55.
    C noise covariance,signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise) Result 3 Whitening Real Noise 55
  • 56.
    • According toSNR (when 16 to 64) - For all SNR, whitened SR case is a little nosier than just SR case Result 3 Whitening Real Noise 56 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
  • 57.
    • According toSNR (when 16 to 64) - For most of SNR, whitened SR case is less correlated than SR case Result 3 Whitening Real Noise 57 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
  • 58.
    • According toSNR (when 16 to 64) - At very low SNR, error distance from whitened SR is reduced Result 3 Whitening Real Noise 58 C noise covariance, signal x = source signal s + noise n xwhitened = C-1/2 x = C-1/2 (s + n) = C-1/2 s + w (white noise)
  • 59.
    Source localization results,when SNR 0.5 Result 3 Whitening Real Noise 59 SR Whitened SR
  • 60.
    Conclusion 3 • Whiteningof real noise - can be effective for SR - especially for source analysis 60
  • 61.
  • 62.
    Discussion 1 • Whysimulation study? - In real EEG, it is difficult to extract only brain signal from its noise - Because of its noise, we don’t know exact dipole locations - We can’t observe the influence of noise type Exact dipole location from simulation data 62
  • 63.
    Discussion 2 white Gaussiannoise real noise • On same SNR - The case of white Gaussian noise seems to be noisier than real noise one - Eye component in the real noise occupied the noise’s overall power - It is difficult to make an equivalent comparison between them 63
  • 64.
    Discussion 3 • Whydoes SR work well at 16 to 128? - Although it is the case of only white Gaussian noise - We can interpret it as the properties of data-driven approach 64
  • 65.
    Discussion 3 - Higher-dimensionalanswer provides us with more fruitful information - But in real noise case, it may not be useful information LR Conv Conv Conv Features ConvT ConvT ConvT Conv Conv HR 13 X 5 kernel 64 filters 13 X 9 kernel 64 filters 7 X 1 kernel 1 filters training : min θ ( 𝐻𝑅 − 𝐿𝑅)2 16 32 64 128 • Our experimental design 65
  • 66.
    Discussion 4 • Whydid we choose a linear function for deep learning? - It is typical to use non-linear functions to extract features hyperbolic tangent function (tanh) rectified linear unit (ReLU) -1 ≤ y ≤ 1 0 ≤ y ≤ ∞ 66
  • 67.
    Discussion 4 • Whydid we choose a linear function for deep learning? - Let’s regard our problem as finding optimal fitted line min θ ( 𝐻𝑅 − 𝐿𝑅)2 67
  • 68.
    Discussion 4 • Whydid we choose a linear function for deep learning? - Let’s regard our problem as finding optimal fitted line min θ ( 𝐻𝑅 − 𝐿𝑅)2 68
  • 69.
    Summary 69 • Deep learningbased SR may be effective on EEG - EEG SR can reduce experimental cost significantly - EEG SR can provide high resolution data without much effort
  • 70.
    Summary 70 • Deep learningbased SR may be effective on EEG - At sensor and source level - During SR, ideal noise can be canceled out => improve signal quality - In real noisy environment, EEG may be acceptably super-resolved - If we know more sensor information, it may be useful for SR - Whitening could be effective for SR • Limitations - However, it has limitation of data-driven approach => need HR data - We need to conduct more experiments on real EEG data
  • 71.
    Publication • EEG super-resolution [1]Sangjun Han, Moonyoung Kwon, Sung Chan Jun, “Feasibility Study of EEG Super-Resolution Using Deep Convolutional Networks,” IEEE International Conference on Systems, Man, and Cybernetics, Oct 2018 (Submitted) [2] Sangjun Han, Moonyoung Kwon, Sunghan Lee, Sung Chan Jun, “EEG Spatial Super-Resolution Using Deep Convolutional Linear Networks : a Simulation Study,” Korean Society of Medical & Biological Engineering, Nov 2017 (Best Paper) • EEG emotion classification using deep learning [3] Sunghan Lee, Sangjun Han, Sung Chan Jun, “EEG-based Classification of Multi-class Emotional States Using One- dimensional Convolutional Neural Networks,” 7th Graz BCI Conference, July 2017 [4] Sunghan Lee, Sangjun Han, Sung Chan Jun, “Four-Class Emotion Classification Using One-dimensional Convolutional Neural Networks - An EEG Study,” Society for Neuroscience, Nov 2017 • Improving sleep quality by acoustic stimulation [5] Jinyoung Choi, Sangjun Han, Moonyoung Kwon, Hyeon Seo, Sehyeon Jang, Sung Chan Jun, “Study on Subject-Specific Parameters in Sleep Spindle Detection Algorithm,” The IEEE Engineering in Medicine and Biology Conference, July 2017 [6] Jinyoung Choi, Sangjun Han, Kyungho Won, Sung Chan Jun, “Effect of Acoustic Stimulation after Sleep Spindle Activity,” Sleep Medicine, Oct 2017 [7] Jinyoung Choi, Sangjun Han, Kyungho Won, Sung Chan Jun, “The Neurophysiological Effect of Acoustic Stimulation with Real-time Sleep Spindle Detection,” The IEEE Engineering in Medicine and Biology Conference, July 2018 Refereed Conference Paper 71
  • 72.
    References [1] D. M.Tucker, “Spatial Sampling of Head Electrical Fields: The Geodesic Sensor Net,” Electroencephalography and Clinical Neurophysiology, vol. 87, pp. 154–163, September 1993. [2] A. Sohrabpour, Y. Lu, P. Kankirawatana, J. Blount, H. Kim, and B. He, “Effect of EEG Electrode Number on Epileptic Source Localization in Pediatric Patients,” Clinical Neurophysiology, vol. 126, pp. 472-480, December 2015. [3] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning Representations by Back-propagating errors,” Nature, vol. 323, pp. 533-536, October 1986. [4] G. E. Hinton, “A Practical Guide to Training Restricted Boltzmann Machines,” Lecture Notes in Department of Computer Science, University of Toronto, August 2010. [5] D. George, Y. Dong, D. Li and A. Alex, “Context-Dependent Pre-Trained Deep Neural Networks for Large- Vocabulary Speech Recognition,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 20, no. 1, pp. 30- 42, January 2012. [6] K. Alex, S. Ilya and H. Geoffrey, “ImageNet Classification with Deep Convolutional Neural Networks,” in Proceedings of the Neural Information Processing Systems, December 2012. [7] C. Dong, C. C. Loy, and X. Tang, “Image Super-Resolution Using Deep Convolutional Networks,” IEEE Transactions on Pattern Analysis and Machie Intelligence, vol. 38, pp. 295–307, June 2015. [8] J. Kim, J. K. Lee, and L. M. Lee, “Deeply-Recursive Convolutional Network for Image Super-Resolution,” Conference on Computer Vision and Pattern Recognition, pp. 1637–1645, June 2016. [9] W. Shi, J. Caballero, F. Huszar, J. Totz, A. P. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” Conference on Computer Vision and Pattern Recognition, pp. 1874–1883, June 2016. [10] C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, amd W. Shi, “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network,” Conference on Computer Vision and Pattern Recognition, pp. 4681–4690, July 2017. [11] V. Kuleshov, S. Z. Enam, and S. Ermon, “Audio Super-Resolution Using Neural Nets,” Workshop of International Conference on Learning Representation, April 2017. [12] I. A. Corley, and Y. Huang, “Deep EEG Super-Resolution: Upsampling EEG Spatial Resolution with Generative Adversarial Networks,” IEEE EMBS International Conference on Biomedical & Health Informatics, March 2018 [13] K. Sekihara, and S. S. Nagarajan, Adaptive Spatial Filters for Electromagnetic Brain Imaging, 1st ed., Springer-Verlag Berlin Heidelberg, 2008. [14] P. Kingma, and J. Ba, “ADAM: A Method for Stochastic Optimization,” International Conference on Learning Representation, arXiv:1412.6980, May 2015. [15] K. He, X, Zhang, S. Ren, and J. Sun, “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,” International Conference on Computer Vision, pp. 1026–1034, December 2015. 72
  • 73.