暫態音誘發性耳聲傳射(click-evoked otoacoustic emission, CEOAE)訊號在臨床上常用於新生兒聽力篩檢，由於CEOAE訊號的強度通常低於背景雜訊，其量測需要以數百、數千次的平均來估測埋藏在雜訊裡的訊號。本論文提出兩個方法來降噪CEOAE訊號：時頻濾波器(time-frequency filtering)與最佳化收縮估計法(optimal shrinkage)，其中最佳估計法有兩種版本：共變異數矩陣為基底與奇異值分解為基底；除此之外本研究也實作了使用適應性步驟找濾波區間的時頻濾波器、最佳化收縮估計法與時頻濾波器的組合、以及兩種針對最佳化收縮估計法的改動：滑動窗口最佳化收縮估計法以及逐塊最佳化收縮估計法。在模擬的CEOAE訊號上，共變異數矩陣的最佳化收縮估計法對比取資料中位數的基本方法，可以穩定增加訊雜比1到2 dB，而奇異值分解的最佳化收縮估計法可以提升3 dB訊雜比、時頻濾波器可以提升6 dB訊雜比。在真實的CEOAE訊號上，奇異值分解的最佳化收縮估計法可以穩定的提升訊雜比，而且原始訊雜比越低提升的幅度就越高；時頻濾波器只對使用非線性量測法的資料有效，而提升的訊雜比優於最佳化收縮估計法。滑動窗口法可以額外增加2 dB訊雜比，而將奇異值分解的最佳化收縮估計法使用在時頻濾波器之前可以額外增加1到2 dB訊雜比。單純考慮CEOAE訊號的降噪，最佳化收縮估計法無法贏過時頻濾波器，但最佳化收縮估計法的優勢是降噪所有訊號而不是只有平均後的訊號，這個特性讓研究長時間CEOAE的動態性成為可能。

Click-evoked otoacoustic emissions (CEOAEs) are clinically used as an objective way to infer whether cochlear functions are normal. However, because the sound pressure level of CEOAEs is typically much lower than the background noise, it usually takes hundreds, if not thousands of repetitions to estimate the signal with sufficient accuracy. In this thesis, we propose to improve the signal-to-noise ratio (SNR) of CEOAE signals within limited measurement time by time-frequency filtering (TF) and optimal shrinkage (OS) in two different settings: covariance-based OS (cOS) and singular value decomposition (SVD)-based OS (sOS). We also implemented Wiener filtering (WF), an adaptive procedure for finding the T-F region for the time-frequency filtering, combined the sOS and the TF, and presented two approaches to improve the performance of sOS: window-based sOS (wOS) and block-wise sOS (bOS). By simulation, the WF and the cOS consistently enhanced the SNR by 1 to 2 dB from a baseline method (BM) that is based on calculating the median. The sOS could enhance the SNR by over 3 dB and the TF even achieved 6 dB enhancement. In real data, the sOS improved the SNR consistently, and the level of enhancement increases as the baseline SNR decreases. The TF only worked on the CEOAE signals measured by nonlinear protocol, and it provides greater SNR enhancement than the sOS. The wOS further improved the SNR by 2 dB from the sOS, and applying sOS before TF further improved the SNR by 1 to 2 dB from the TF. For the denosing of CEOAE signals, the performance of TF is better than OS. Nonetheless, an appealing property of OS is that it produces an estimate of all single trials. This property makes it possible to investigate CEOAE dynamics across a longer period of time when the cochlear conditions are not strictly stationary.

誌謝i
摘要ii
Abstract iii
1 Introduction 1
1.1 Motivation 2
1.2 Existing methods 5
1.3 Optimal shrinkage 6
1.4 Summary of main contributions 8
2 Mathematical methods for CEOAE signal estimation 9
2.1 Covariance-based optimal shrinkage 9
2.2 SVD-based optimal shrinkage 11
2.3 Wiener filtering 12
2.4 TF filtering 13
2.5 Hybrid method 13
2.6 Moving-window sOS 14
2.7 Block-wise sOS 15
2.8 Summaries of OS mathematics 16
2.8.1 Derivation of cOS for the Frobenius norm loss 17
2.8.2 Derivation of sOS for the Frobenius norm loss 18
3 Materials 21
3.1 CEOAE measurement 21
3.1.1 Measurement in Cathay Hospital 21
3.1.2 Measurement at NTHU 22
3.2 Segmentation and signal quality determination 24
3.3 Generation of simulated CEOAE 24
4 Experiments and results 26
4.1 Observation of singular values 27
4.2 Observation of time-frequency regions 27
4.3 Denoising simulated CEOAE 29
4.4 Denoising real CEOAE 33
4.4.1 Linear protocol 33
4.4.2 Nonlinear protocol 38
4.5 Denoising SSOAE 42
5 Discussion 47
5.1 Signal processing perspective of optimal shrinkage as a filter 47
5.2 Behavior of optimal shrinkage on real CEOAEs 48
5.3 Behavior of time-frequency filtering on real CEOAEs 49
5.4 Overall comparison between denoising methods 50
5.4.1 Comparison of sOS and TF 50
5.4.2 Combination of sOS and TF 51
5.4.3 Moving-window and block-wise sOS 51
5.5 Other issues 52
5.5.1 Issue about noise estimation 52
5.5.2 Presence of SSOAEs in CEOAE signals 53
5.5.3 Investigating the CEOAE dynamics 54
5.6 Remaining problems and future works 54
5.6.1 Modification of recording procedure 54
5.6.2 Improving the adaptive procedure for finding the TF
region 55
5.6.3 Further evaluation for the denoising methods 55
5.6.4 Investigation after CEOAE denoising 56
6 Conclusion 58
References 60

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