Wireless neural recording systems are subject to stringent power consumption constraints to support long-term recordings and to allow for implantation inside the brain. In this paper, we propose using a combination of on-chip detection of action potentials (“spikes”) and compressive sensing (CS) techniques to reduce the power consumption of the neural recording system by reducing the power required for wireless transmission. We empirically verify that spikes are compressible in the wavelet domain and show that spikes from different neurons acquired from the same electrode have subtly different sparsity patterns or supports. We exploit the latter fact to further enhance the sparsity by incorporating a union of these supports learned over time into the spike recovery procedure. We show, using extracellular recordings from human subjects, that this mechanism improves the SNDR of the recovered spikes over conventional basis pursuit recovery by up to 9.5 dB (6 dB mean) for the same number of CS measurements. Though the compression ratio in our system is contingent on the spike rate at the electrode, for the datasets considered here, the mean ratio achieved for 20-dB SNDR recovery is improved from 26:1 to 43:1 using the learned union of supports.
http://nesl.ee.ucla.edu/document/show/364
3. Full Implantability
Put the exam room IN the patient !
Cyberkinetics Neurotechnology Systems/Matthew McKee Utah Electrode Array
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4. Raw Signal from a Depth Electrode
[uwhealth.org]
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5. Signal Band Pass Filtered to Enhance Spikes
Filtering
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6. Spike Detection
Detection
These spikes are from
multiple neurons in the
vicinity of the electrode
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9. Traditional Wireless Neural Recording Process
In vivo
Amplify Band Pass Spike Detect Radio
and Digitize Filter and Align TX
Radio Spike
RX Sorting
Ex vivo
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10. CS Neural Recording Process
In vivo
Amplify Band Pass Spike Detect Compressive Radio
and Digitize Filter and Align Sampling TX
Radio CS Spike
RX Recovery Sorting
Add
Support
Ex vivo
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11. Two Features Useful for Compressed Sensing
‣ Spikes are compressible in the wavelet domain
‣ Spikes from the same neuron are similar in morphology
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12. Representing the Spike in DWT Domain
Few large coefficients in
DWT domain --
compressible
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13. Number of Significant Coefficients (Support) in
DWT Domain
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21. size of the support computed over 600 000 spikes extracted
from the entire dataset. About Recovery describe the action
Compressed Sensing 8 coefficients
potential adequately, a compression of 6:1 from the raw 48
samples acquired per spike.
y
We can now formulate our recovery procedure as the basis
m
pursuit denoising (BPDN) [5] problem:
1 −1 2
z = argmin y − ΦΨ z
ˆ ˜ 2
+λ z
˜ 1 (2)
z 2
˜
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22. size of the support computed over 600 000 spikes extracted
from the entire dataset. About Recovery describe the action
Compressed Sensing 8 coefficients
potential adequately, a compression of 6:1 from the raw 48
samples acquired per spike.
y
We can now formulate our recovery procedure as the basis
m
pursuit denoising (BPDN) [5] problem:
1 −1 2
z = argmin y − ΦΨ z
ˆ ˜ 2
+λ z
˜ 1 (2)
z 2
˜
−1
ˆ ˆ
x=Ψ z
n
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23. CS Neural Recording Process
In vivo
Amplify Band Pass Spike Detect Compressive Radio
and Digitize Filter and Align Sampling TX
Radio CS Spike
RX Recovery Sorting
Ex vivo
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24. Conventional Basis Pursuit Results
3rd Quartile
Median over 0.6M spikes
1st Quartile
35.7 measurements for
20dB SNDR
18x → 26x compression
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25. Two Features Useful for Compressed Sensing
‣ Spikes are compressible in the wavelet domain
‣ Spikes from the same neuron are similar in morphology
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26. Similarity in Neural Spikes
Little support mismatch,
Mismatch at low values
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27. potential adequately, a compression of 6:1 from the raw 48
samples acquired per spike.
We can now formulate our recovery Recovery the basis
Incorporating Similarity in CS procedure as
pursuit denoising (BPDN) [5] problem:
Basis Pursuit Recovery
1 −1 2
z = argmin y − ΦΨ z
ˆ ˜ 2
+λ z
˜ 1 (2)
z 2
˜
Φ - Sampling matrix
Ψ - Sparsifying transform
λ - L1 penalizing factor
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28. potential adequately, aΦΨ−1 satisfies a condition known a
the ensemble matrix compression of 6:1 from the raw 48
samples acquired per spike.
the restricted isometry property (RIP) [5], the error in th
Incorporating SimilaritywillCS Recovery the basis
formulate our in be procedure as
We can nowabove problemrecoverystable and bounded wit
solution to the
pursuit denoising (BPDN) [5] problem:
overwhelming probability.
Basis Pursuit Recovery
1
In [7], Lu=and Vaswani−introduced + λnew approach t
−1 2 a
z argmin y ΦΨ z 2
ˆ ˜ z 1
˜ (2)
z 2
BPDN called Modified-CS when additional knowledge i
˜
available. Specifically, they show that if the support of th
Φ - Sampling matrix
spike -waveform (or a part thereof) was known a priori, th
Ψ Sparsifying transform
λ - L1 penalizing factor
error in the solution to Eq. (2) admits a lower bound. Thei
modified BPDN approach is given by:
Masked Basis Pursuit Recovery
1 −1 2
z = argmin y − ΦΨ z 2 + λ zT c 1
ˆ ˜ ˜ (3
z 2
˜
c
where, T is the complement of the known support so zT ˜
denotes the elements in z that are not included within T . Th
˜
bound on the 2 norm of the solution error depends on λ 20 an
zainul@ee.ucla.edu - Spike CS - May 2011
29. potential adequately, aΦΨ−1 satisfies a condition known a
the ensemble matrix compression of 6:1 from the raw 48
samples acquired per spike.
the restricted isometry property (RIP) [5], the error in th
Incorporating SimilaritywillCS Recovery the basis
formulate our in be procedure as
We can nowabove problemrecoverystable and bounded wit
solution to the
pursuit denoising (BPDN) [5] problem:
overwhelming probability.
Basis Pursuit Recovery
1
In [7], Lu=and Vaswani−introduced + λnew approach t
−1 2 a
z argmin y ΦΨ z 2
ˆ ˜ z 1
˜ (2)
z 2
BPDN called Modified-CS when additional knowledge i
˜
available. Specifically, they show that if the support of th
Φ - Sampling matrix
spike -waveform (or a part thereof) was known a priori, th
Ψ Sparsifying transform
λ - L1 penalizing factor
error in the solution to Eq. (2) admits a lower bound. Thei
modified BPDN approach is given by:
Masked Basis Pursuit Recovery
1 −1 2
z = argmin y − ΦΨ z 2 + λ zT c 1
ˆ ˜ ˜ (3
z 2
˜
T - Set of support indices expected in the spike known support so zT
c
where, T is the complement of the ˜
Tc - Set of support indices not expected sparser than support itself
denotes the elements in z that are not included within T . Th
˜ [Wang, et. al., 2010; Vaswani et. al., 2010, Charbiwala, 2009]
bound on the 2 norm of the solution error depends on λ 20
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30. Learning a Union of Supports Results in Very
Low Sparsity
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31. Learning a Union of Supports Results in Very
Low Sparsity
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32. Learning a Union of Supports Results in Very
Low Sparsity
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33. CS Neural Recording Process
In vivo
Amplify Band Pass Spike Detect Compressive Radio
and Digitize Filter and Align Sampling TX
Radio CS Spike
RX Recovery Sorting
Add
Support
Ex vivo
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34. Learned Union of Support Results
22.1 measurements for
20dB SNDR
18x → 43x compression
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36. Stability of Union Progression
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37. 8 25
Size of Union of Supports
7 20
Why Union CS Works
6 15
Error bound
5 10
4 I nc re asi ng |∆|, Fi x e d |∆ e| 5
I nc re asi ng |∆|, D e c re asi ng |∆ e|
3 0
0 100 200 300 400 500 600
Fi x e d |∆|, I nc re asi ng |∆ e|
2 #Spikes
D e c re asi ng |∆|, I nc re asi ng |∆ e| Fig. 5. Median progression of the size of the learn
1 each set of 1000 spikes.
2 4 6 8 10 12 14 16 18 20
Size of support set 4
x 10
2.5
Fig. 4. Trend lines of the error bound that trade off the size of the unknown
Norm Outside
#Spike Occurences
support, ∆ with the size of the superfluous support, ∆e . The curves illustrate 2 Norm Outside
the sensitivity of the error bound on |∆| and the relative insensitivity to |∆e |. µ = 0 . 036, σ= 0. 037
1.5
We provide two justifications for our union of supports
1 µ = 0. 2 72, σ= 0. 167
proposal, one derived analytically and one empirically from
Δ : Number ofthe first, Negativesthe Unknown Support 0.5
our datasets. For False we excerpt -- bound on modified
Δe : Number of False Positives -- Superfluous Support 00 Adding to superfluous set is 0.6
BPDN reconstruction error from [7]:
0.1 0.2 0.3 0.4 0.5
2
θ|T |,|∆| alright if unknown support Norm
1
z − z 2 ≤ λ |∆|
ˆ 2 +1 2
Fig. 6. set is reducing norm of signal outside
Histogram of the at same pace
θ|T |,|∆|
1 − δ|T | 1 − δ|∆| − 1−δ|T | and outside learned union of support of all preced
σ 2 sizes of the two sets. We defer a full an
+ (4) of the error bound performance for futur
1 − δ|N ∪∆e |
Fig. 5 shows the progression of the size
where |·| refers to set cardinality, δs is the s-restricted isometry 2011 T over our datasets. In order to co
set
zainul@ee.ucla.edu - Spike CS - May
constant constant [5] for the matrix ensemble ΦΨ−1 and θ
26
38. Spike Sorting Performance
U. Rutishauser, , A. Mamelak, and E. Schuman, “Online detection and sorting of extracellularly recorded action potentials in human
medial temporal lobe recordings, in vivo,” Journal of Neuroscience Methods, vol. 154, pp. 204–224, 2006.
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39. Clustering Performance
Original CS Neural Recording
16 measurements for
90% clustering accuracy
18x → 56x compression
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41. Conclusions and Future Directions
‣ 2x compression versus sensing raw spikes at low power
‣ Sorting possible on compressed version at lower rates
‣ In development: 8-channel FPGA based implementation
‣ Within the year: ASIC based 16-channel solution
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42. Thank You !
Slides, Code, Data @
http://nesl.ee.ucla.edu/people/zainul
44. Magnitude of Coefficients of Consecutive
Spikes are Dissimilar
Spikes differ by 90%
on the average in DWT
domain
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45. Magnitude of Mismatched Coefficients in
Consecutive Spikes is Lower
Spikes are 70% sparser
outside support of
previous spike
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46. Magnitude of Mismatched Coefficients from
All Previous Spikes is Very Low
Spikes are 95% sparser
outside support of all
previous spikes
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Good morning. My name is Zainul Charbiwala and I’m going to present a compressed sensing solution for wireless neural recording. The language of neurons are the action potentials or spikes and neuroscientists want to capture as much of this neuronal activity as possible. \n
