Unbiased coherent-to-diffuse ratio estimation for dereverberation

Abstract

We investigate the estimation of the time-and frequencydependent coherent-to-diffuse ratio (CDR) from the measured spatial coherence between two omnidirectional microphones. We illustrate the relationship between several known CDR estimators using a geometric interpretation in the complex plane, discuss the problem of estimator bias, and propose unbiased versions of the estimators. Furthermore, we show that knowledge of either the direction of arrival (DOA) of the target source or the coherence of the noise field is sufficient for an unbiased CDR estimation. Finally, we apply the CDR estimators to the problem of dereverberation, using automatic speech recognition word error rate as objective performance measure.

An analysis of environment, microphone and data simulation mismatches in robust speech recognition

“…They reported this beamformer to perform similarly on real and simulated data, which is particularly noticeable as it contributed to their entry winning the challenge. A few challenge entries also employed multichannel dereverberation techniques based on time-domain linear prediction (Yoshioka et al, 2010) or interchannel coherence-based time-frequency masking (Schwarz and Kellermann, 2014). As expected, these techniques improved performance on real data but made a smaller difference or even degraded performance on simulated data due to the fact that it did not include any early reflection or reverberation (Yoshioka et al, 2015;Barfuss et al, 2015;Pang and Zhu, 2015).…”

Coherent-to-Diffuse Power Ratio Estimation for Dereverberation

“…Solving (9) for the CDR yields (for brevity, the time-and frequency-dependency is omitted in the following) (15) or, reformulated as the diffuseness ,…”

“…The bias of a CDR estimator is henceforth defined as the deviation of the estimator from (15) for coherence values along this line; i.e., an unbiased estimator should exactly match (15) for these values. This can be verified by inserting according to (15) for into the estimator equation, which yields for an unbiased estimator. Furthermore, since the coherence estimates , which are observed in practice, will not lie exactly on the line, a good estimator should also be robust in the sense that some deviations of the coherence estimate from the assumed model, e.g., caused by an imperfect DOA estimate, do not lead to large deviations of the CDR estimate.…”

“…Thiergart et al [11], [13] proposed to estimate the CDR by directly inserting the target signal coherence estimate into (15), and taking the real part: (18) While this estimator is unbiased, it was found to be very sensitive towards phase deviations of the coherence estimate from the ideal model [13]. For a measured coherence with a magnitude close to one, even a small phase difference between and can have a large effect on the CDR estimate.…”

“…Also, results have since been generalized from omnidirectional microphones to other microphone directivities [12], [13] and spherical microphone arrays [14]. While these estimates can be used for the formulation of postfilters for signal enhancement [15], which is the main application considered in this contribution, short-time CDR estimates (or the equivalent "diffuseness" measure) also have applications in parametric coding of spatial audio signals [16] and the extraction of spatial features for automatic speech recognition (ASR) [17].…”