Denoising click-evoked otoacoustic emission signals by optimal shrinkage

Optimal Scale-Invariant Wavelet Representation and Filtering of Human Otoacoustic Emissions

Otoacoustic emissions (OAEs) are generated in the cochlea and recorded in the ear canal either as a time domain waveform or as a collection of complex responses to tones in the frequency domain (Probst et al. J Account Soc Am 89:2027-2067, 1991). They are typically represented either in their original acquisition domain or in its Fourier-conjugated domain. Round-trip excursions to the conjugated domain are often used to perform filtering operations in the computationally simplest way, exploiting the convolution theorem. OAE signals consist of the superposition of backward waves generated in different cochlear regions by different generation mechanisms, over a wide frequency range. The cochlear scaling symmetry (cochlear physics is the same at all frequency scales), which approximately holds in the human cochlea, leaves its fingerprints in the mathematical properties of OAE signals. According to a generally accepted taxonomy (Sher and Guinan Jr, J Acoust Soc Am 105:782-798, 1999), OAEs are generated either by wave-fixed sources, moving with frequency according with the cochlear scaling (as in nonlinear distortion) or by place-fixed sources (as in coherent reflection by roughness). If scaling symmetry holds, the two generation mechanisms yield OAEs with different phase gradient delay: almost null for wave-fixed sources, and long (and scaling as 1/f) for place-fixed sources. Thus, the most effective representation of OAE signals is often that respecting the cochlear scale-invariance, such as the time-frequency domain representation provided by the wavelet transform. In the time-frequency domain, the elaborate spectra or waveforms yielded by the superposition of OAE components from different generation mechanisms assume a much clearer 2-D pattern, with each component localized in a specific and predictable region. The wavelet representation of OAE signals is optimal both for visualization purposes and for designing filters that effectively separate different OAE components, improving both the specificity and the sensitivity of OAE-based applications. Indeed, different OAE components have different physiological meanings, and filtering dramatically improves the signal-to-noise ratio.

Robust estimation of synchronized spontaneous otoacoustic emission via singular value decomposition and optimal shrinkage

We investigate matrix signal processing techniques for estimating synchronized spontaneous otoacoustic emission (OAE) in noise. Responses to repeated clicks are first stored in a matrix, and singular value decomposition is either applied in the time domain or the frequency domain after constructing a Hankel matrix at every frequency. The singular values are subject to optimal shrinkage (OS) which maximizes the signal-to-noise ratio. Human OAE data were analyzed, and the Hankel matrix method outperforms the time-domain OS method in synchronized spontaneous otoacoustic emission estimation, but not in the estimation of transient-evoked otoacoustic emission. Reasons for the performance discrepancy are discussed.

Measuring Distortion-Product Otoacoustic Emission With a Single Loudspeaker in the Ear: Stimulus Design and Signal Processing Techniques

The distortion-product otoacoustic emission (DPOAE) is a backward propagating wave generated inside the cochlea during the wave amplification process. The DPOAE signal can be detected rapidly under relatively noisy conditions. In recent years, the earphone industry demonstrated interest in adopting DPOAE as an add-on feature to make their product “intelligent” of inner-ear status. However, a technical challenge remains to be tackled—the loudspeaker in an earphone generates its own cubic distortion at the same frequency as DPOAE. Unfortunately, the intensity of loudspeaker distortion is typically comparable to that of the DPOAE, if not higher. In this research, we propose two strategies, namely compensation and cancellation, to enable DPOAE measurement with a single loudspeaker. The compensation strategy exploits the part of the growth function of the loudspeaker distortion which is almost linear, and thus suppresses the distortion it generates while retaining a larger portion of DPOAE in the residual signal. The cancellation strategy utilizes a one-dimensional Volterra filter to remove the cubic distortion from the loudspeaker. Testing on normal-hearing ears shows that the compensation strategy improved the DPOAE-to-interference ratio by approximately 7 dB, resulting in a cross-correlation of 0.62 between the residual DPOAE level and the true DPOAE level. Meanwhile, the cancellation strategy directly recovered both the magnitude and the phase of DPOAE, reducing the magnitude estimation error from 15.5 dB to 3.9 dB in the mean-square sense. These pilot results suggest that the cancellation strategy may be suitable for further testing with more subjects.