Spike-Based Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept

Transcription

1 Spike-Based Sensing and Processing: What are spikes good for? John G. Harris Electrical and Computer Engineering Dept ONR NEURO-SILICON WORKSHOP, AUG 1-2, 2006

2 Take Home Messages Introduce integrate-and-fire (IF) signal coding x(t) Spiking Neuron Model y( t i ) IF coding improves sensor performance IF is an alternative to traditional Nyquist sampling and can achieve perfect reconstruction IF is a power- and bandwidth-efficient strategy (outperforms rate codes) We can process these spikes within a mathematical framework (see Jose Principe s talk)

3 Transmit analog value Noise problems Case 1: DC Signals Digitize to N bits and transmit Requires ADC Rate code Too much bandwidth, too much power Timing code send two spikes

4 Integrate and fire coding Applications: Imager x(t) Potentiostat y ( t i ) C V ref

5 Dynamic Range Dynamic range quantifies the ability to image bright and dark areas simultaneously.

6 L I G H T CMOS Imagers Dynamic Range Limitation C I V V V res NOISE FLOOR V = I t C 0 t Dynamic range 60-70dB

7 Using Rate Coding V = t (I/C) L I G H T C I V V V res V ref NOISE FLOOR 0 t Dynamic range extended to ~140dB.

8 Rate Coding Schemes Advantages: Each pixel chooses its own integration time to optimize noise and dynamic range No analog readout noise No A/D required Disadvantages: Takes too long to form an image (~seconds) Wasteful in terms of power and bandwidth Bright pixel Dark pixel

9 Using Time-To-First-Spike Coding V = t (I/C) L I G H T C I V V V res V ref NOISE FLOOR 0 t Dynamic range extended to ~140dB.

10 Dynamically Adjusting the Threshold V = t (I/C) L I G H T C I V V V res V ref NOISE FLOOR 0 T t Dynamic range extended to ~140dB within time T.

11 Summary of Time-to-First-Spike Coding Advantages: Each pixel chooses its own integration time to optimize noise and dynamic range No analog readout noise No A/D required Low power and small bandwidth Parallels in biology (Simon Thorpe)

12 Prototype Chip Technology: 0.5 µm AMI CMOS Supply Voltage: 5 Volt Transistors per pixel: 30 Array size: 32 x 32 Pixel size: 38µm x 35µm Photosensitive area: 5µm x 5µm Power dissipation: 3.1 mw at 30fps (without pad power) Dark current: 1.25 na/cm 2 Dynamic Range: 140 db (one pixel, measured) Dynamic Range: 104 db (array, measured), limited by the optics

13 Reading Pixel Data Off-chip Uses a variation of Address Event Representation (AER), as discussed by K. Boahen. When a pixel fires its row and column address are multiplexed onto an output bus. Need low spike rate to prevent collisions

14 128x128 Imager in 0.18um CMOS

15 Basic Potentiostat Design I ΔT = CΔV I in

16 Chip Results Analytic vs. Measured Results Measured Specifications: Offset: 5mV Detection limit: 1pA Dynamic range: 116dB Area: 0.025mm 2 Power: 130uW Sensitivity:100fA

17 Case 2: Positive AC Signals x(t) time Signal x(t) is bandlimited to Ω s

18 Standard Nyquist Rate Sampling x(t) T < π Ω s 0 T 2T 3T 4T 5T 6T 7T 8T 9T time Amplitude sampling: record amplitude at predefined time intervals.

19 Standard Nyquist Rate Sampling x(t) T < π Ω s time How to perfectly reconstruct the signal from the samples?

20 Standard Nyquist Rate Sampling x(t) T < π Ω s time The signal is perfectly reconstructed by ideal low-pass filtering the samples using well-known Nyquist theory.

21 Sampling With Integrate-and-fire (IF) Neuron Model x(t) time Signal x(t) is bandlimited to Ω s

22 Sampling With Integrate-and-fire (IF) Neuron Model x(t) Encoding equation t time t i 1 + x( t) dt = t i θ Define the integral: f ( t) = t t 0 x( τ ) dτ

23 Sampling With Integrate-and-fire (IF) Neuron Model f (t) 11θ 10θ 9θ 8θ 7θ 6θ 5θ 4θ 3θ 2θ θ t0 1 2 Define the integral: ( t) The sample time t i meet: f 9 = 10 t t 0 11 time x( τ ) dτ f ( ti ) = iθ Encoding equation t i 1 + x( t) dt = t i θ

24 Sampling With Integrate-and-fire (IF) Neuron Model f (t) 11θ 10θ 9θ 8θ 7θ 6θ 5θ 4θ 3θ 2θ θ Encoding equation t i 1 + x( t) dt = t i θ t time Time sampling: record time at predefined amplitude intervals.

25 Sampling With Integrate-and-fire (IF) Neuron Model Spike T max < π Ω s Encoding equation 1 + x( t) dt = t t i i θ T max time Can low-pass filtering achieve perfect reconstruction? No. Signal band is corrupted by cross-modulated components (Bayly 68).

26 Signal Reconstruction Any bandlimited signal can be expressed as a lowpass filtered version of an appropriately weighted sum of delayed impulse functions. (Derived from Duffin et al. 1952, Feichtinger et al. 1994, Lazar et al.) Signal Impulse train Lowpass Filter Amplitude Time Weight Δt max < π Ω s Time = = xt () ht ()* wδ ( t s) wht ( s) * Ω s Mag j j j j j j Where w j is computed by solving a linear system 1 Ωs Freq

27 Simulation Results (Matlab) X(t) is a Gaussian random noise signal bandlimited to 1.5kHz Maximum ISI = 0.14ms < T SNR = 103dB SNR is limited by the finite number of spikes and finite computational precision

28 Temporal Quantization 110 SNR (db) Clock Period (S) Shows the effect of temporal quantization on SNR. Temporal quantization happens when the spike train is synchronized to a fast clock on a DSP. The plot also gives an idea of how much timing jitter can be allowed in the electronics and in the transmission

29 Frequency Aliasing Shows the effect of frequency aliasing on SNR. SNR (db) Aliasing Freq (Hz) Standard Nyquist Rate Sampling Can we reconstruct the signal from a neuron chip? For IF neuron, the detrimental effect of high frequency aliasing is reduced because of the integration. For standard Nyquist rate sampling, higher frequencies are simply mapped to lower frequencies preserving its power.

30 Integrate-and-fire Neuron Chip Fabricated in AMI C5 0.5u CMOS process V/I converter and IF neuron on the chip

31 Integrate-and-fire Neuron Circuit Implementation Modified Mead Neuron

32 Chip Test Results SNR v.s. Signal freq. 80 SNR (db) Average firing rate is about 100kHz. SNR is above 63dB (Using IEEE std 1241) Power is (66uA)(5V) = 330uW. Have now reached < 50uW (still unoptimized) 0 0 5k 10k 15k 20k 25k 30k Signal Freq. (Hz)

33 Extends to Other Neuron Models Works with refractory period (to limit peak spiking rate) Leaky IF neuron models: Spice simulation of CMOS LIF neurons shows reconstruction SNR > 80dB Neuron with adaptation:

34 Applications 1. ADC replacement 2. Neural amplifier Applications in remote sensing, implanted devices and power-limited systems. Simpler analog circuitry on the remote sensor is traded off for more complex digital reconstruction on the bay station. Simple and low power Robust to transmission noise

35 Bio-amplifier with Pulse Output Input signal: Signal amplitudes: uV Frequency range: 100Hz-6kHz Local Field Potential < 1Hz DC offset of 1-2V Must be low-noise, lowpower and compact

36 Measured Spike Data Input 20uV sinusoid Signal amplified by 100 Spikes are output and reconstructed

37 Measured Performance Midband gain: db Low freq cutoff: ~300mHz High freq cutoff: 5.4kHz Input referred noise: 9.56uVrms Power consumption: 300uW CMRR: >-59.2 db PSRR: ~45 db Dynamic Range: 52.7dB Output DC offset: ~100mV Die area: 0.088mm^2/channel Amplitude (mv) Time (second) Measured in vivo recording (voltage output)

38 Case 3: Signed AC Signals Vth+ + τ P + (t) Vin Gm C Vth- + τ P-(t) Vmid OR P + (t) P-(t) Biphasic pulse coding

39 Measured Chip Data 1 (a) Voltage (mv) Voltage (mv) x 10-3 (b) x 10-3 (c) Time (s) x 10-3 AMI 0.5um CMOS process 100 uw power consumption

40 Sub-Nyquist Rate Sampling (Simulation) Original Fs = 25 khz 18 kspikes/sec 9 kspikes/sec 6 kspikes/sec

41 Conclusions Introduced integrate-and-fire (IF) signal coding IF coding improves sensor performance IF is an alternative to traditional Nyquist sampling and can achieve perfect reconstruction IF is a power- and bandwidth-efficient strategy (outperforms rate codes) We can process these spikes within a mathematical framework (see Jose Principe s talk) Questions?