By Elvir Causevic Department of Applied Mathematics Yale University Founder and President

1. Fast Wavelet Estimation of Weak Biosignals By Elvir Causevic Department of Applied Mathematics Yale University Founder and President Everest Biomedical Instruments

2. Overview • Introduction and Motivation • Human auditory system • Measurement of auditory function and difficulties in signal processing • Introduction to wavelets and conventional wavelet denoising • Novel wavelet denoising algorithm • Frame recombination • Denoising • Variable threshold selection • Estimation of rate of convergence • Experimental results • Future work • Conclusion and summary

3. Introduction • Overall goal • Creation of a fast estimator of weak biosignals based on wavelet signal processing. Application to auditory brainstem responses (ABRs) and other evoked potentials • Specific objectives • Reduce the length of time to acquire a valid ABR signal. • Allow ABR signal acquisition in a noisy environment. • Key obstacles • Very large amount of acoustical and electrical noise present . • Signals collected from ear and brain have very low SNR and require long averaging times

4. Infant Hearing Screening • Infant hearing screening is critically important in early intervention of treating deafness. • Hearing loss affects 3 in 1,000 infants: most commonly occurring birth defect. • 25,000 hearing impaired babies born annually in the U.S. alone. • Lack of early detection often leads to permanent loss of ability to acquire normal language skills. • Early detection allows intervention that commonly results in development of normal speech by school age. • Intervention involves hearing aids, cochlear implants and extensive parent and child education and training. • 38 U.S. states mandate hearing screening, Europe, Australia, Asia following closely.

5. Measurement of Hearing Function • Auditory Brainstem Response (ABR) - neural test • Response of the VIIIth nerve - auditory neuro-pathway to brain VIIIth Nerve

6. Auditory Brainstem Response (ABR)Signal Processing & Clinical Issuesfor Infant Hearing Screening • Stimulus: 37 clicks per second, 65 dB SPL (30 dB nHL). • Response: scalp electrodes measure μV level signals. • Noise: completely buries the response (-35dB). • Pass: signal to noise ratio measure (called Fsp) greater than an experimentally determined value (NIH Multicenter study). • With linear averaging, reliable results are obtained within ~15 minutes of averaging of ~ 4000-8000 frames at a single level. • We would like to test multiple levels (up to 10) , and with multiple tone pips (vs. clicks). This test normally takes over an hour, in a sound attenuated booth, manually administered by an expert. • Currently only a single level response is tested and only a pass/fail result is provided, with over 5% false positive rate. • Substantial improvement in rate of signal averaging is required to obtain a full diagnostic and reliable test.

7. Auditory Brainstem Response example

9. Infant Hearing Screening Space Limitations Time Constraints Patient Tracking Electrical Noise Acoustic Noise

10. Auditory Brainstem Response (ABR)Signal Processing & Clinical Issues Frequency domain characteristics of a typical ABR click stimulus as measured in the ear using the ER-10C transducer

11. Auditory Brainstem Response (ABR)Signal Processing & Clinical Issues

12. Linear Averaging • Linear averaging - sample mean estimate • Linear averaging increases the amplitude SNR by a factor of N1/2 • Cramer Rao lower bound on variance

13. Linear Averaging Comparison of Fsp values with and without stimulus presentation

14. Traditional Fourier Transform Representation of signals in orthonormal basis using complex exponentials (real and imaginary sinusoidal components). Signal represented in frequency domain by a one-dimensional sequence. “Loses” time information. Features like transients, drifts, trends, etc. may be lost upon reconstruction. Wavelet Transform Representation of signals in unconditional orthonormal basis using waveforms of limited durations with average value of zero. Makes no assumption about length or periodicity of signals. Contains time information in coefficients Signal can be fully reconstructed using inverse transform, and local time features are preserved. Wavelet Basics

15. Wavelet Transform • Discrete wavelet transform (DWT) (α = scale coefficient, β=translation coefficient)

16. Example Wavelet Filters

17. Wavelet Decomposition Example

18. Conventional Wavelet Denoising • Conventional denoising • Perform wavelet transform. • Set coefficients |C(α,β)|<δ to zero, δ – threshold value. These coefficients are more likely to represent noise than signal. • Perform inverse wavelet transform. • Characteristics of conventional denoising • Assumes that signal is smooth and coherent, noise rough and incoherent. • Operation is performed on a single frame of data. • Non-linear operation – reduces the coefficients differently depending on their amplitude.

19. Conventional Wavelet Denoising • Why does wavelet denoising work? • The underlying signal is smooth and coherent, while the noise is rough and incoherent • A function f(t) is smooth if • A function f(t) is smooth to a degree d, if • Bandlimited functions are smooth • Measured biologic functions are smooth (such as ABR)

20. Conventional Wavelet Denoising • Coherent vs. incoherent • A signal is coherent if its energy is concentrated in both time and frequency domains. • A reasonable measure of coherence is the percentage of wavelet coefficients required to represent 99% of signal energy. • An example well-concentrated signal may require 5% of coefficients to represent 99% of its energy. • Completely incoherent noise requires 99% of coefficients to represent 99% of its energy.

21. Conventional Wavelet Denoising

22. Conventional Wavelet Denoising

23. Novel Wavelet Denoising • Conventional denoising applied to weak biosignals • Setting coefficients |C(α,β)|< δ to zero, effectively removes all the coefficients, including the ones that represent the signal. • SNR must be large (>20dB). • Novel Wavelet Denoising • Take advantage of multiple frames of data available. • Create new frames through recombination and denoising. • Apply a different δkfor each new set of recombined frames. Proprietary confidential information

24. Tree Denoising • Create a tree • Collect a set of N frames of original data [f1, f2, …, fN] • Take the first two frames of the signal, f1 and f2, and average together, f12= (f1+f2)/2 • Denoise this average f12 using a threshold δk , fd12=den(f12 ,δ1). • Linearly average together two more frames of the signal, f34 ,and denoise that average, fd34=den(f34 ,δ1). Continue this process for all N frames • Create a new level of frames consisting of [fd12, fd34, …, fdN-1,N]. • Linearly average each two adjacent new frames to create f1234=(fd12 +fd34), and denoise that average to create fd1234=den(f1234 ,δ2). • Continue to apply in a tree like fashion. • Apply a different δk for denoising frames at each new level. Proprietary confidential information

25. Tree Denoising Graph Proprietary confidential information

26. Cyclic Shift Tree Denoising (CSTD) Proprietary confidential information

27. Cyclic Shift Tree Denoising (CSTD) Original signal Denoise with δ1 k=1  Denoise with δ2 k=2 …  Denoise with δ3 … …  Denoise with δk Final level Proprietary confidential information

28. Frame Permutations • - Create new arrangements of original frames prior to CSTD • xnew=(p*xold) mod N • Increase total number of new frames by a factor of 0.5*N*log2(N) Proprietary confidential information

29. Threshold Selection Proprietary confidential information

30. Estimated Rate of Convergence • Linear averaging - sample mean estimate • CSTD Creates M=log2(N)*N new frames. • Permutations prior to CSTD create at most M=0.5*(N2 * log2(N) new frames. • CSTD can improve the Cramer-Rao lower bound by at most a factor of 0.5*N*log2(N). • The new frames are not linearly dependent, but also not all statistically independent.

31. Experimental ResultsNoisy Sinewaves Proprietary confidential information

32. Experimental ResultsABR Data

33. Experimental ResultsABR Data

34. V Pa Pb Na Time (ms) (a) Nb (b) (c) (e) (d) Experimental ResultsAMLR Data Performance of CSTD algorithm compared to linear averaging 256 data frames. (a): Template of AMLR evoked potential waveform from Spehlmann; (b): linear average of 8192 AMLR frames; (c): Single frame consisting of AMLR model plus WGN; (d): Linear average of 256 frames; (e): Result of CSTD algorithm

35. The Final Product

36. Future Work & Other applications • Wavelet denoising using wavelet packets • EEG/EP Recording and Monitoring • Use in ambulances and emergency rooms • At-home patient monitoring • Depth of Anesthesia Monitoring • Monitor brain stem and cortex activity during surgery • Use in all operating rooms • Oto-toxic drug administration • Certain strong antibiotics cause hearing loss - ototoxic • Dosage can be monitored on-line • Use in intensive care units

37. ED Bedside in minutes Non-patient care Environment-hours

39. HLB PRELIMINARY CONCEPT

40. HLB PRELIMINARY CONCEPT

41. Thank you! • Questions?

42. Experimental ResultsNoisy Sinewaves Proprietary confidential information

43. Example Wavelet Filters An additional property of a basis is being unconditional. A basis {φn} is an unconditional basis for a normed space if there is some constant C<∞ such that for coefficients cn, and any sequence {εn} of zeros and ones. This means that if some coefficients cn are set to zero by the sequence {εn}, the norm of the remaining series is always bounded. Sines and cosines are NOT unconditional bases.