同步自發性耳聲傳射是瞬時誘發耳聲傳射衰減後產生的持續震盪，瞬時誘發耳聲傳射則是耳朵的脈衝響應，可以由短暫音刺激產生。同步自發性耳聲傳射具有監控暫時聽力損失的潛力，因此準確估計並取得高訊噪比的訊號是相當重要的。可用於估計瞬時誘發耳聲發射的一種技術稱為奇異質最佳收縮法，此方法是基於奇異值分解，且透過收縮奇異值大小以達成降噪目的，奇異值的最佳收縮比例可透過最小化損失函數求得，例如 Frobenius 範數。然而，此方法在壓抑同步自發性耳聲傳射訊號的隨機雜訊能力表現不佳，因此在本篇研究中，我們提出了改良版本，運用了頻率域漢克爾矩陣的奇異值分解，並透過最佳收縮法來提升估計同步自發性耳聲傳射的準確度。由於漢克爾矩陣反斜對角線上具有相同元素，故此方法首先會在每一個頻率進行漢克爾矩陣的奇異值分解，並且使用最佳收縮器調整奇異值大小，然後再透過於矩陣反斜對角線取中位數的方式，來取得估測訊號，最後再將訊號轉換回到時域。本篇論文發現，改良版本的演算法於雜訊較高的環境下在提升估測訊號訊噪比表現優異，在同步自發性耳聲傳射方面，改良版本的演算法對比資料取平均的基本方法，在僅分析前100次量測下，可以提升2.26 dB訊噪比。

Synchronized spontaneous (SS) otoacoustic emission (OAE) is the response of the cochlea after transient evoked (TE) OAE decays. TEOAE is the impulse response of the cochlea that can be evoked by a short stimulus. SSOAE has shown potential for monitoring hearing loss. As a result, it is crucial to achieve a high signal-to-noise ratio (SNR) in the estimate of the SSOAE signal. One existing technique used to estimate TEOAE is called optimal shrinkage (OS) of singular values. This method is based on singular value decomposition (SVD), and it denoises the data by shrinking the singular values. This optimal shrinker can be derived by minimizing different types of loss functions, such as the Frobenius norm. Nevertheless, the conventional approach does not perform well in suppressing random noise in the SSOAE spectra. In this thesis, we propose a modified algorithm which performs SVD of Hankel matrices in the frequency domain and applies OS techniques to improve the estimation of SSOAE. Hankel matrix is a special type of matrix that has constant values along each descending anti-diagonal. Therefore, the proposed algorithm first performs SVD on each Hankel matrix that is constructed at each frequency bin; subsequently the singular values are optimally shrunk. Following that, we take the median over each descending anti-diagonal to have an estimate of the SSOAE spectrum. Finally, we compute the inverse Fourier transform to acquire an estimate in the time domain. Our results suggest that this modification has the potential to be an effective noise reduction algorithm for use in noisy environments. When only the first 100 trials were used in the denoising, the proposed algorithm could enhance the SNR by 2.26 dB from an artifact rejection method that is based on calculating the mean.

[1] D. T. Kemp, “Stimulated acoustic emissions from within the human auditory
system,” The Journal of the Acoustical Society of America, vol. 64, no. 5,
pp. 1386–1391, 1978.
[2] R. Fettiplace and C. M. Hackney, “The sensory and motor roles of auditory
hair cells,” Nature Reviews Neuroscience, vol. 7, no. 1, pp. 19–29, 2006.
[3] M. Penner and T. Zhang, “Prevalence of spontaneous otoacoustic emissions in
adults revisited,” Hearing Research, vol. 103, no. 1-2, pp. 28–34, 1997.
[4] W. W. Jedrzejczak, K. J. Blinowska, K. Kochanek, and H. Skarzynski, “Syn-
chronized spontaneous otoacoustic emissions analyzed in a time-frequency
domain,” The Journal of the Acoustical Society of America, vol. 124, no. 6,
pp. 3720–3729, 2008.
[5] S. Marchesi, G. Tognola, and A. Paglialonga, “A bispectral approach to an-
alyze nonlinear cochlear active mechanisms in transient evoked otoacoustic
emissions,” IEEE Transactions on Biomedical Circuits and Systems, vol. 7,
no. 4, pp. 401–413, 2013.
[6] D. T. Kemp, “Otoacoustic emissions, travelling waves and cochlear mecha-
nisms,” Hearing Research, vol. 22, no. 1-3, pp. 95–104, 1986.
[7] M. A. Hotz, R. Probst, F. P. Harris, and R. Hauser, “Monitoring the effects
of noise exposure using transiently evoked otoacoustic emissions,” Acta Oto-
Laryngologica, vol. 113, no. 4, pp. 478–482, 1993.
[8] A. J. Hall and M. E. Lutman, “Methods for early identification of noise-
induced hearing loss,” Audiology, vol. 38, no. 5, pp. 277–280, 1999.
[9] P. Kumar, K. Kumar, and A. Barman, “Effect of short duration broad band
noise on transient evoked otoacoustic emission amplitude,” Indian Journal of
Otolaryngology and Head & Neck Surgery, vol. 65, no. 1, pp. 44–47, 2013.
[10] J. Attias. and I. Bresloff., “Noise induced temporary otoacoustic emission
shifts,” Journal of Basic and Clinical Physiology and Pharmacology, vol. 7,
no. 3, pp. 221–234, 1996.
[11] B. M. Vinck, P. B. Van Cauwenberge, L. Leroy, and P. Corthals, “Sensitivity
of transient evoked and distortion product otoacoustic emissions to the direct
effects of noise on the human cochlea,” Audiology, vol. 38, no. 1, pp. 44–52,
1999.
[12] P. K. Plinkert, W. Hemmert, W. Wagner, K. Just, and H. P. Zenner, “Moni-
toring noise susceptibility: Sensitivity of otoacoustic emissions and subjective
audiometry,” British Journal of Audiology, vol. 33, no. 6, pp. 367–382, 1999.
[13] S. P. Bhagat and A. M. Davis, “Modification of otoacoustic emissions follow-
ing ear-level exposure to mp3 player music,” International Journal of Audiol-
ogy, vol. 47, no. 12, pp. 751–760, 2008.
41
[14] M. L. Whitehead, B. B. Stagner, B. L. Lonsbury-Martin, and G. K. Martin,
“Measurement of otoacoustic emissions for hearing assessment,” IEEE Engi-
neering in Medicine and Biology Magazine, vol. 13, no. 2, pp. 210–226, 1994.
[15] M. Gavish and D. L. Donoho, “Optimal shrinkage of singular values,” IEEE
Transactions on Information Theory, vol. 63, no. 4, pp. 2137–2152, 2017.
[16] T.-C. Liu, Y.-W. Liu, and H.-T. Wu, “Denoising click-evoked otoacoustic emis-
sion signals by optimal shrinkage,” Journal of the Acoustical Society of Amer-
ica, vol. 149, no. 4, pp. 2659–2670, 2021.
[17] B. Liu and Q. Liu, “Random noise reduction using svd in the frequency do-
main,” Journal of Petroleum Exploration and Production Technology, vol. 10,
pp. 3081–3089, 2020.
[18] W. Bi, Y. Zhao, C. An, and S. Hu, “Clutter elimination and random-noise de-
noising of gpr signals using an svd method based on the hankel matrix in the
local frequency domain,” Sensors, vol. 18, no. 10, p. 3422, 2018.
[19] Z. Liu, W. Zhao, X. Chen, Z. Hao, and Z. Li, “Local svd for random noise sup-
pression of seismic data in frequency domain,” Shiyou Diqiu Wuli Kantan/Oil
Geophysical Prospecting, vol. 47, no. 2, p. 202–206, 2012.
[20] D. T. Kemp, P. Bray, L. Alexander, and A. M. Brown, “Acoustic emission
cochleography–practical aspects,” Scandinavian Audiology. Supplementum,
vol. 25, pp. 71–95, 1986.
[21] A. Boul and B. Lineton, “Spontaneous otoacoustic emissions measured using
an open ear-canal recording technique,” Hearing Research, vol. 269, no. 1-2,
pp. 112–121, 2010.