The Colour of Noise

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My presentation at the Good Noise in Neural Computation symposium of the 2018 Organization for Human Brain Mapping annual meeting.

Science

Outline
1. Colours
2. Dithering
3. Noise
4. Colours of Noise
5. Where is Good Noise?

Colours
Above and Beyond. “Common Ground.” Anjuna Beats, 2018.

Colours
Stockman, MacLeod & Johnson. “Simplified human cone response
curves” Journal of the Optical Society of America. 1993.
Wavelength (nm)
Response

Colours
Adobe Systems Inc. “Adobe RGB (1998) Color Image Encoding”.
May 2005.

Dithering
Doyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive
Computational Neuroscience, 2018. (under review)
colours gray ramp
Floyd-Steinberg (1976)

Noise
𝑦 𝑡 = 𝑥 𝑡 + ε
measurement signal noise

Aliasing
Ghosh, S. “Aliasing”.
https://nbviewer.jupyter.org/urls/dl.dropbox.com/s/s0nw827nc4kcnaa/
Aliasing.ipynb, 2018.
Original

Aliasing
Subsampled Anti-aliased
https://nbviewer.jupyter.org/urls/dl.dropbox.com/s/s0nw827nc4kcnaa/
Aliasing.ipynb

Assigning a colour to noise means:
1. Amplitude is Gaussian distributed
2. Particular Power Spectral Density (PSD)
Colours of Noise

Colours of Noise
What colourDoyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive
Computational Neuroscience, 2018. (under review)

Doyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive
Computational Neuroscience, 2018. (under review)
Colours of Noise

Colours of Noise
Colour Power Spectral Distribution
Black 1/𝑓 𝛼, 𝛼 > 2
Gray
121942
⋅ 𝑓4
𝑓2 + 20.62 √(𝑓2 + 737.92)(𝑓2 + 121942)
Brown 1/𝑓2
Orange musical notes removed
Red 1/𝑓2
Pink 1/𝑓
White 𝑐
Green 1/𝑓2
or 𝑐
Blue 𝑓
Violet 𝑓2

Pink Noise
Yukti, S. “Action Potential Animal Systems”. SlideShare.
slideshare.net/dryuktisharma/action-potentials-animal-systems. 2014.
1
𝑓

Pink Noise
Gao, R. “Interpreting the Electrophysiological Power
Spectrum”. Journal of Neurophysiology, 2015.
1
𝑓
ECoG

$Pink Noise Pritchard, Walter S. "The brain in fractal time: 1/f-like power spectrum scaling of the human electroencephalogram." International Journal of Neuroscience 66.1-2 (1992): 119-129. EEG 1 𝑓$

Pink Noise
Zhou, Junhong, et al. "Pink noise: effect on complexity
synchronization of brain activity and sleep consolidation." Journal of
theoretical biology 306 (2012): 68-72
1
𝑓
Stochastic Facilitation
with audio

Blue Noise
𝑓
Mitsa, Theophano, and Kevin J. Parker. "Digital halftoning technique
using a blue-noise mask." JOSA A 9.11 (1992)

Blue Noise
Yellott, John I. "Spectral consequences of photoreceptor sampling in
the rhesus retina." Science 221.4608 (1983): 382-385.

Blue Noise
Georgiev, I et al. “Blue-noise Dithered Sampling.” SIGGRAPH, 2016.
𝑓

Noise in Vision
Kuriki,Ichiro,etal."FunctionalbrainimagingoftheRotating
SnakesillusionbyfMRI."Journalofvision8.10(2008):16-16.

Signals and Noise
𝑦 𝑡 = 𝑥 𝑡 + ε
𝑦 𝑡 = 𝑋 𝑡 + ε
deterministic
random / stochastic / noise / variable

Signals and Noise
𝑦 𝑡 = 𝑥 𝑡 + ε
𝑦 𝑡 = 𝑥 𝑡 + gn(t) + ε
deterministic

Signals and Noise
𝑦 𝑡 = 𝑥 𝑡 + ε
𝑦 𝑡 = 𝑥 𝑡, 𝑔𝑛 + gn(t) + ε
deterministic

Measuring Noise
1. Variance
2. Number of PCA components
3. Multiscale Entropy (MSE)
McIntosh, Anthony R., et al. "The development of a noisy
brain." Archives italiennes de biologie 148.3 (2010): 323-337.

Distraction
Cohen, Marlene R., and John HR Maunsell. "Attention improves
performance primarily by reducing interneuronal
correlations." Nature neuroscience 12.12 (2009): 1594.

fMRI
PyBIDS
Gorgolewski, Krzysztof J., et al. "A test-retest fMRI dataset for motor,
language and spatial attention functions." GigaScience2.1 (2013): 6.

Noise & Stability
Halley, John M., and Pablo Inchausti. "The increasing importance of
1/f-noises as models of ecological variability." Fluctuation and Noise
Letters 4.02 (2004): R1-R26.

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The Colour of Noise

1. The Colour of Noise Andrew Doyle @crocodoyle McGill Centre for Integrative Neuroscience

2. Outline 1. Colours 2. Dithering 3. Noise 4. Colours of Noise 5. Where is Good Noise?

3. Colours Above and Beyond. “Common Ground.” Anjuna Beats, 2018.

4. Colours Stockman, MacLeod & Johnson. “Simplified human cone response curves” Journal of the Optical Society of America. 1993. Wavelength (nm) Response

5. Colours Adobe Systems Inc. “Adobe RGB (1998) Color Image Encoding”. May 2005.

6. Colours Adobe Systems Inc. “Adobe RGB (1998) Color Image Encoding”. May 2005.

7. Dithering Doyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive Computational Neuroscience, 2018. (under review) colours gray ramp Floyd-Steinberg (1976)

8. Dithering

9. Noise 𝑦 𝑡 = 𝑥 𝑡 + ε measurement signal noise

10. Noise

11. Noise

12. Noise

13. Noise

14. Noise

15. Noise

16. Noise + Dithering

17. Noise

18. Aliasing Ghosh, S. “Aliasing”. https://nbviewer.jupyter.org/urls/dl.dropbox.com/s/s0nw827nc4kcnaa/ Aliasing.ipynb, 2018. Original

19. Aliasing Subsampled Anti-aliased https://nbviewer.jupyter.org/urls/dl.dropbox.com/s/s0nw827nc4kcnaa/ Aliasing.ipynb

20. Assigning a colour to noise means: 1. Amplitude is Gaussian distributed 2. Particular Power Spectral Density (PSD) Colours of Noise

21. Colours of Noise What colourDoyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive Computational Neuroscience, 2018. (under review)

22. Doyle, JA, Evans, AC. “What Colour is Neural Noise?” Cognitive Computational Neuroscience, 2018. (under review) Colours of Noise

23. Colours of Noise Colour Power Spectral Distribution Black 1/𝑓 𝛼, 𝛼 > 2 Gray 121942 ⋅ 𝑓4 𝑓2 + 20.62 √(𝑓2 + 737.92)(𝑓2 + 121942) Brown 1/𝑓2 Orange musical notes removed Red 1/𝑓2 Pink 1/𝑓 White 𝑐 Green 1/𝑓2 or 𝑐 Blue 𝑓 Violet 𝑓2

24. Pink Noise Yukti, S. “Action Potential Animal Systems”. SlideShare. slideshare.net/dryuktisharma/action-potentials-animal-systems. 2014. 1 𝑓

25. Pink Noise Gao, R. “Interpreting the Electrophysiological Power Spectrum”. Journal of Neurophysiology, 2015. 1 𝑓 ECoG

26. Pink Noise Pritchard, Walter S. "The brain in fractal time: 1/f-like power spectrum scaling of the human electroencephalogram." International Journal of Neuroscience 66.1-2 (1992): 119-129. EEG 1 𝑓

27. Pink Noise Zhou, Junhong, et al. "Pink noise: effect on complexity synchronization of brain activity and sleep consolidation." Journal of theoretical biology 306 (2012): 68-72 1 𝑓 Stochastic Facilitation with audio

28. Blue Noise 𝑓 Mitsa, Theophano, and Kevin J. Parker. "Digital halftoning technique using a blue-noise mask." JOSA A 9.11 (1992)

29. Blue Noise Yellott, John I. "Spectral consequences of photoreceptor sampling in the rhesus retina." Science 221.4608 (1983): 382-385.

30. Blue Noise Yellott, John I. "Spectral consequences of photoreceptor sampling in the rhesus retina." Science 221.4608 (1983): 382-385.

31. Blue Noise Yellott, John I. "Spectral consequences of photoreceptor sampling in the rhesus retina." Science 221.4608 (1983): 382-385.

32. Blue Noise Georgiev, I et al. “Blue-noise Dithered Sampling.” SIGGRAPH, 2016. 𝑓

33. Gizmodo

34. Noise in Vision Kuriki,Ichiro,etal."FunctionalbrainimagingoftheRotating SnakesillusionbyfMRI."Journalofvision8.10(2008):16-16.

35. Signals and Noise 𝑦 𝑡 = 𝑥 𝑡 + ε 𝑦 𝑡 = 𝑋 𝑡 + ε deterministic random / stochastic / noise / variable

36. Signals and Noise 𝑦 𝑡 = 𝑥 𝑡 + ε 𝑦 𝑡 = 𝑥 𝑡 + gn(t) + ε deterministic

37. Signals and Noise 𝑦 𝑡 = 𝑥 𝑡 + ε 𝑦 𝑡 = 𝑥 𝑡, 𝑔𝑛 + gn(t) + ε deterministic

38. Where to Look

39. Measuring Noise 1. Variance 2. Number of PCA components 3. Multiscale Entropy (MSE) McIntosh, Anthony R., et al. "The development of a noisy brain." Archives italiennes de biologie 148.3 (2010): 323-337.

40. Distraction Cohen, Marlene R., and John HR Maunsell. "Attention improves performance primarily by reducing interneuronal correlations." Nature neuroscience 12.12 (2009): 1594.

41. Experiments

42. fMRI PyBIDS Gorgolewski, Krzysztof J., et al. "A test-retest fMRI dataset for motor, language and spatial attention functions." GigaScience2.1 (2013): 6.

43. EEG

44. Noise & Stability Halley, John M., and Pablo Inchausti. "The increasing importance of 1/f-noises as models of ecological variability." Fluctuation and Noise Letters 4.02 (2004): R1-R26.

45. Conclusion

46. https://github.com/crocodoyle/good-noise

47. Conclusion

48. Conclusion

The Colour of Noise

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