Compressively Sensing   Action Potentials    (Neural Spikes)Zainul Charbiwala, Vaibhav Karkare, Sarah Gibson        Dejan ...
Full ImplantabilityCyberkinetics Neurotechnology Systems/Matthew McKee                                              Utah E...
Full Implantability                                                                       Put the exam room IN the patient...
Raw Signal from a Depth Electrode[uwhealth.org]                  zainul@ee.ucla.edu - Spike CS - May 2011   3
Signal Band Pass Filtered to Enhance Spikes                              Filtering               zainul@ee.ucla.edu - Spik...
Spike Detection                                Detection                                                              Thes...
Spike Alignment                                Alignment                  zainul@ee.ucla.edu - Spike CS - May 2011   6
Spike Sorting                                Sorting                zainul@ee.ucla.edu - Spike CS - May 2011   7
Traditional Wireless Neural Recording Process In vivo                Amplify        Band Pass            Spike Detect     ...
CS Neural Recording Process In vivo                Amplify        Band Pass            Spike Detect          Compressive  ...
Two Features Useful for Compressed Sensing‣   Spikes are compressible in the wavelet domain‣   Spikes from the same neuron...
Representing the Spike in DWT Domain                    Few large coefficients in                       DWT domain --      ...
Number of Significant Coefficients (Support) inDWT Domain                zainul@ee.ucla.edu - Spike CS - May 2011   12
Sparsity Inducing Transform                                                          x                           n        ...
Sparsity Inducing Transform                                                          x                           n        ...
Sparsity Inducing Transform                                                          x                           n        ...
A Visual Tour of Compressed Sensing                                                          x                           n...
A Visual Tour of Compressed Sensing                                                          x                           n...
A Visual Tour of Compressed Sensing                                                          x                           n...
Compressed Sensing Recovery                                                         y                  m              zain...
size of the support computed over 600 000 spikes extractedfrom the entire dataset. About Recovery describe the action   Co...
size of the support computed over 600 000 spikes extractedfrom the entire dataset. About Recovery describe the action   Co...
CS Neural Recording Process In vivo                Amplify        Band Pass            Spike Detect          Compressive  ...
Conventional Basis Pursuit Results                                                                  3rd Quartile          ...
Two Features Useful for Compressed Sensing‣   Spikes are compressible in the wavelet domain‣   Spikes from the same neuron...
Similarity in Neural Spikes                                                            Little support mismatch,           ...
potential adequately, a compression of 6:1 from the raw 48samples acquired per spike.  We can now formulate our recovery R...
potential adequately, aΦΨ−1 satisfies a condition known athe ensemble matrix      compression of 6:1 from the raw 48 sample...
potential adequately, aΦΨ−1 satisfies a condition known athe ensemble matrix      compression of 6:1 from the raw 48 sample...
Learning a Union of Supports Results in VeryLow Sparsity                zainul@ee.ucla.edu - Spike CS - May 2011   21
Learning a Union of Supports Results in VeryLow Sparsity                zainul@ee.ucla.edu - Spike CS - May 2011   21
Learning a Union of Supports Results in VeryLow Sparsity                zainul@ee.ucla.edu - Spike CS - May 2011   21
CS Neural Recording Process In vivo                Amplify        Band Pass            Spike Detect          Compressive  ...
Learned Union of Support Results                                                           22.1 measurements for          ...
Comparison with Oracle Support Knowledge              zainul@ee.ucla.edu - Spike CS - May 2011   24
Stability of Union Progression                zainul@ee.ucla.edu - Spike CS - May 2011   25
8                                                                                                 25                      ...
Spike Sorting PerformanceU. Rutishauser, , A. Mamelak, and E. Schuman, “Online detection and sorting of extracellularly re...
Clustering Performance       Original                                              CS Neural Recording                    ...
Power Consumption Comparison             zainul@ee.ucla.edu - Spike CS - May 2011   29
Conclusions and Future Directions‣   2x compression versus sensing raw spikes at low power‣   Sorting possible on compress...
Thank You !        Slides, Code, Data @http://nesl.ee.ucla.edu/people/zainul
Backup Slides
Magnitude of Coefficients of ConsecutiveSpikes are Dissimilar                                                           Sp...
Magnitude of Mismatched Coefficients inConsecutive Spikes is Lower                                                        ...
Magnitude of Mismatched Coefficients fromAll Previous Spikes is Very Low                                                  ...
Comparison with Modified-CS              zainul@ee.ucla.edu - Spike CS - May 2011   36
Sorting Performance with Modified-CS               zainul@ee.ucla.edu - Spike CS - May 2011   37
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Compressively Sensing Action Potentials (Neural Spikes) - Presented at BSN 2011

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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

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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
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  • Compressively Sensing Action Potentials (Neural Spikes) - Presented at BSN 2011

    1. 1. Compressively Sensing Action Potentials (Neural Spikes)Zainul Charbiwala, Vaibhav Karkare, Sarah Gibson Dejan Marković, Mani B. Srivastava In collaboration with UCLA Neuroscience
    2. 2. Full ImplantabilityCyberkinetics Neurotechnology Systems/Matthew McKee Utah Electrode Array zainul@ee.ucla.edu - Spike CS - May 2011 2
    3. 3. Full Implantability Put the exam room IN the patient !Cyberkinetics Neurotechnology Systems/Matthew McKee Utah Electrode Array zainul@ee.ucla.edu - Spike CS - May 2011 2
    4. 4. Raw Signal from a Depth Electrode[uwhealth.org] zainul@ee.ucla.edu - Spike CS - May 2011 3
    5. 5. Signal Band Pass Filtered to Enhance Spikes Filtering zainul@ee.ucla.edu - Spike CS - May 2011 4
    6. 6. Spike Detection Detection These spikes are from multiple neurons in the vicinity of the electrode zainul@ee.ucla.edu - Spike CS - May 2011 5
    7. 7. Spike Alignment Alignment zainul@ee.ucla.edu - Spike CS - May 2011 6
    8. 8. Spike Sorting Sorting zainul@ee.ucla.edu - Spike CS - May 2011 7
    9. 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 zainul@ee.ucla.edu - Spike CS - May 2011 8
    10. 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 zainul@ee.ucla.edu - Spike CS - May 2011 9
    11. 11. Two Features Useful for Compressed Sensing‣ Spikes are compressible in the wavelet domain‣ Spikes from the same neuron are similar in morphology zainul@ee.ucla.edu - Spike CS - May 2011 10
    12. 12. Representing the Spike in DWT Domain Few large coefficients in DWT domain -- compressible zainul@ee.ucla.edu - Spike CS - May 2011 11
    13. 13. Number of Significant Coefficients (Support) inDWT Domain zainul@ee.ucla.edu - Spike CS - May 2011 12
    14. 14. Sparsity Inducing Transform x n zainul@ee.ucla.edu - Spike CS - May 2011 13
    15. 15. Sparsity Inducing Transform x n DWT - Ψ zainul@ee.ucla.edu - Spike CS - May 2011 13
    16. 16. Sparsity Inducing Transform x n DWT - Ψ z= Ψ x n zainul@ee.ucla.edu - Spike CS - May 2011 13
    17. 17. A Visual Tour of Compressed Sensing x n zainul@ee.ucla.edu - Spike CS - May 2011 14
    18. 18. A Visual Tour of Compressed Sensing x n m Φ zainul@ee.ucla.edu - Spike CS - May 2011 14
    19. 19. A Visual Tour of Compressed Sensing x n m Φ y= Φ x m zainul@ee.ucla.edu - Spike CS - May 2011 14
    20. 20. Compressed Sensing Recovery y m zainul@ee.ucla.edu - Spike CS - May 2011 15
    21. 21. size of the support computed over 600 000 spikes extractedfrom the entire dataset. About Recovery describe the action Compressed Sensing 8 coefficientspotential adequately, a compression of 6:1 from the raw 48samples acquired per spike. y We can now formulate our recovery procedure as the basis mpursuit denoising (BPDN) [5] problem: 1 −1 2 z = argmin y − ΦΨ z ˆ ˜ 2 +λ z ˜ 1 (2) z 2 ˜ zainul@ee.ucla.edu - Spike CS - May 2011 15
    22. 22. size of the support computed over 600 000 spikes extractedfrom the entire dataset. About Recovery describe the action Compressed Sensing 8 coefficientspotential adequately, a compression of 6:1 from the raw 48samples acquired per spike. y We can now formulate our recovery procedure as the basis mpursuit 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 zainul@ee.ucla.edu - Spike CS - May 2011 15
    23. 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 zainul@ee.ucla.edu - Spike CS - May 2011 16
    24. 24. Conventional Basis Pursuit Results 3rd Quartile Median over 0.6M spikes 1st Quartile 35.7 measurements for 20dB SNDR 18x → 26x compression zainul@ee.ucla.edu - Spike CS - May 2011 17
    25. 25. Two Features Useful for Compressed Sensing‣ Spikes are compressible in the wavelet domain‣ Spikes from the same neuron are similar in morphology zainul@ee.ucla.edu - Spike CS - May 2011 18
    26. 26. Similarity in Neural Spikes Little support mismatch, Mismatch at low values zainul@ee.ucla.edu - Spike CS - May 2011 19
    27. 27. potential adequately, a compression of 6:1 from the raw 48samples acquired per spike. We can now formulate our recovery Recovery the basis Incorporating Similarity in CS procedure aspursuit 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 zainul@ee.ucla.edu - Spike CS - May 2011 20
    28. 28. potential adequately, aΦΨ−1 satisfies a condition known athe 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 witsolution 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 2BPDN called Modified-CS when additional knowledge i ˜available. Specifically, they show that if the support of th Φ - Sampling matrixspike -waveform (or a part thereof) was known a priori, th Ψ Sparsifying transform λ - L1 penalizing factorerror in the solution to Eq. (2) admits a lower bound. Theimodified 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 ˜ cwhere, 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. 29. potential adequately, aΦΨ−1 satisfies a condition known athe 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 witsolution 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 2BPDN called Modified-CS when additional knowledge i ˜available. Specifically, they show that if the support of th Φ - Sampling matrixspike -waveform (or a part thereof) was known a priori, th Ψ Sparsifying transform λ - L1 penalizing factorerror in the solution to Eq. (2) admits a lower bound. Theimodified 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 cwhere, T is the complement of the ˜ Tc - Set of support indices not expected ­ sparser than support itselfdenotes 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 zainul@ee.ucla.edu - Spike CS - May 2011 an
    30. 30. Learning a Union of Supports Results in VeryLow Sparsity zainul@ee.ucla.edu - Spike CS - May 2011 21
    31. 31. Learning a Union of Supports Results in VeryLow Sparsity zainul@ee.ucla.edu - Spike CS - May 2011 21
    32. 32. Learning a Union of Supports Results in VeryLow Sparsity zainul@ee.ucla.edu - Spike CS - May 2011 21
    33. 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 zainul@ee.ucla.edu - Spike CS - May 2011 22
    34. 34. Learned Union of Support Results 22.1 measurements for 20dB SNDR 18x → 43x compression zainul@ee.ucla.edu - Spike CS - May 2011 23
    35. 35. Comparison with Oracle Support Knowledge zainul@ee.ucla.edu - Spike CS - May 2011 24
    36. 36. Stability of Union Progression zainul@ee.ucla.edu - Spike CS - May 2011 25
    37. 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 fromΔ : Number ofthe first, Negativesthe Unknown Support 0.5 our datasets. For False we excerpt -- bound on modifiedΔe : 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. 38. Spike Sorting PerformanceU. Rutishauser, , A. Mamelak, and E. Schuman, “Online detection and sorting of extracellularly recorded action potentials in humanmedial temporal lobe recordings, in vivo,” Journal of Neuroscience Methods, vol. 154, pp. 204–224, 2006. zainul@ee.ucla.edu - Spike CS - May 2011 27
    39. 39. Clustering Performance Original CS Neural Recording 16 measurements for 90% clustering accuracy 18x → 56x compression zainul@ee.ucla.edu - Spike CS - May 2011 28
    40. 40. Power Consumption Comparison zainul@ee.ucla.edu - Spike CS - May 2011 29
    41. 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 zainul@ee.ucla.edu - Spike CS - May 2011 30
    42. 42. Thank You ! Slides, Code, Data @http://nesl.ee.ucla.edu/people/zainul
    43. 43. Backup Slides
    44. 44. Magnitude of Coefficients of ConsecutiveSpikes are Dissimilar Spikes differ by 90% on the average in DWT domain zainul@ee.ucla.edu - Spike CS - May 2011 33
    45. 45. Magnitude of Mismatched Coefficients inConsecutive Spikes is Lower Spikes are 70% sparser outside support of previous spike zainul@ee.ucla.edu - Spike CS - May 2011 34
    46. 46. Magnitude of Mismatched Coefficients fromAll Previous Spikes is Very Low Spikes are 95% sparser outside support of all previous spikes zainul@ee.ucla.edu - Spike CS - May 2011 35
    47. 47. Comparison with Modified-CS zainul@ee.ucla.edu - Spike CS - May 2011 36
    48. 48. Sorting Performance with Modified-CS zainul@ee.ucla.edu - Spike CS - May 2011 37

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