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Fig. 8. Gain curves for the MMSE STSA estimators incorporating speech presence uncertainty (SPU) with q = 0.2. (a) GY (Gaussian speech prior) defined by (36), (b) G’Y (Laplacian speech prior) defined by (37), (c) Gey (Gamma speech prior) defined by ()39, and (d) the respective Ephraim and Malah solution Gat (complex Gaussian speech prior), as seen in [(30)] [6].

Figure 8 Gain curves for the MMSE STSA estimators incorporating speech presence uncertainty (SPU) with q = 0.2. (a) GY (Gaussian speech prior) defined by (36), (b) G’Y (Laplacian speech prior) defined by (37), (c) Gey (Gamma speech prior) defined by ()39, and (d) the respective Ephraim and Malah solution Gat (complex Gaussian speech prior), as seen in [(30)] [6].

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Classification of the MMSE estimators with respect to transform domain. The noise is assumed to be additive and Gaussian. * indicate estimators for which no exact closed-form solutions exist. Table 1
Classification of the MMSE estimators with respect to transform domain. The noise is assumed to be additive and Gaussian. * indicate estimators for which no exact closed-form solutions exist. Table 1
Fig. 1. Perceived quality estimation for Polarity-Only (PO, solid line), Phase-Only (PhO, dashed line) and noisy (dotted line) stimuli as a function Segmental SNR.
Fig. 1. Perceived quality estimation for Polarity-Only (PO, solid line), Phase-Only (PhO, dashed line) and noisy (dotted line) stimuli as a function Segmental SNR.
Fig. 2. Mean preference scores (with standard error bars) for four stimuli types at: (a) —5 dB, (b) 0 dB, and (c) 5 dB Segmental SNR (SegSNR)
Fig. 2. Mean preference scores (with standard error bars) for four stimuli types at: (a) —5 dB, (b) 0 dB, and (c) 5 dB Segmental SNR (SegSNR)
Fig. 3. Gain curves (with é = y — 1) describing: DCT MMSE spectral amplitude estimator with Gaussian prior Gy (é,y) defined by (15), indicated with solid line; the Ephraim and Malah solution [6] Gey (complex Gaussian speech prior), indicated with dashed line; Wiener filter solution Gy defined by (19) (Gaussian speech prior, linear filter), indicated with dash-dotted line. Nevertheless, the computation of (25) for a wide dynamic range is not trivial, and numerical problems may result when the arguments are large. To improve numerical stability, we rewrite (25) in terms of the modified Bessel functions (see Appendix C) spectral coefficient estimators always suppress more noise than the corresponding spectral amplitude estimators.
Fig. 3. Gain curves (with é = y — 1) describing: DCT MMSE spectral amplitude estimator with Gaussian prior Gy (é,y) defined by (15), indicated with solid line; the Ephraim and Malah solution [6] Gey (complex Gaussian speech prior), indicated with dashed line; Wiener filter solution Gy defined by (19) (Gaussian speech prior, linear filter), indicated with dash-dotted line. Nevertheless, the computation of (25) for a wide dynamic range is not trivial, and numerical problems may result when the arguments are large. To improve numerical stability, we rewrite (25) in terms of the modified Bessel functions (see Appendix C) spectral coefficient estimators always suppress more noise than the corresponding spectral amplitude estimators.
where ¢, =sgn(A_), I.,(Z) and K,(z) denote the modified Bessel functions of the first and second kind, respectively [eq.9.6.1] [42]. Similar to the Laplacian case, there is no closed-form solution for the equivalent DFT-based MMSE spectral amplitude estimator when the Gamma PDF is used [9,15]. Fig. 5 illustrates the gain
where ¢, =sgn(A_), I.,(Z) and K,(z) denote the modified Bessel functions of the first and second kind, respectively [eq.9.6.1] [42]. Similar to the Laplacian case, there is no closed-form solution for the equivalent DFT-based MMSE spectral amplitude estimator when the Gamma PDF is used [9,15]. Fig. 5 illustrates the gain
Fig. 4. Gain curves (with € = y — 1) describing: DCT MMSE spectral amplitude estimator with Laplacian prior G, defined by (22), indicated with solid line; DFT MMSE spectral amplitude estimator [9] G,_gs4 with v = 1 and K = 20 (i.e., the Taylor series of the modified Bessel function was truncated after 20 terms), indicated with dashed line; DCT MMSE spectral coefficient estimator with Laplacian speech prior [18] G,_csc, indicated with dashed-dotted line; DFT MMSE spectral coefficient estimator [14] G,_rsc with v = 1 and K = 20, indicated with dotted line. MATLAB implementations of the algorithms presented in [9,14] are available at [41].
Fig. 4. Gain curves (with € = y — 1) describing: DCT MMSE spectral amplitude estimator with Laplacian prior G, defined by (22), indicated with solid line; DFT MMSE spectral amplitude estimator [9] G,_gs4 with v = 1 and K = 20 (i.e., the Taylor series of the modified Bessel function was truncated after 20 terms), indicated with dashed line; DCT MMSE spectral coefficient estimator with Laplacian speech prior [18] G,_csc, indicated with dashed-dotted line; DFT MMSE spectral coefficient estimator [14] G,_rsc with v = 1 and K = 20, indicated with dotted line. MATLAB implementations of the algorithms presented in [9,14] are available at [41].
Fig. 5. Gain curves (with € = y — 1) describing: DCT MMSE spectral amplitude estimator with Gamma prior G, defined by (27), indicated with solid line; DFT MMSE spectral amplitude estimator [9] Gc_gs, with v = 0.6 and K = 20 (i.e., the Taylor series of the modified Bessel function was truncated after 20 terms), indicated with dashed line; DCT MMSE spectral coefficient estimator with Gamma speech prior [18] Gc_csc, indicated with dashed-dotted line; DFT MMSE spectral coefficient estimator [14] Gc_psc with y = 0.6 and K = 20, indicated with dotted line. MATLAB implementations of the algorithms presented in [9,14] are available at [41].
Fig. 5. Gain curves (with € = y — 1) describing: DCT MMSE spectral amplitude estimator with Gamma prior G, defined by (27), indicated with solid line; DFT MMSE spectral amplitude estimator [9] Gc_gs, with v = 0.6 and K = 20 (i.e., the Taylor series of the modified Bessel function was truncated after 20 terms), indicated with dashed line; DCT MMSE spectral coefficient estimator with Gamma speech prior [18] Gc_csc, indicated with dashed-dotted line; DFT MMSE spectral coefficient estimator [14] Gc_psc with y = 0.6 and K = 20, indicated with dotted line. MATLAB implementations of the algorithms presented in [9,14] are available at [41].
Fig. 6. Gain curves plotted against the a priori SNR é and the instantaneous SNR y — 1 for the MMSE STSA estimators: (a) Gy (Gaussian speech prior) defined by (15), (b) G, (Laplacian speech prior) defined by (22), (c) Gc (Gamma speech prior) defined by (27), and (d) the Ephraim and Malah solution Ggy (complex Gaussian speech prior), as seen in [(14)] [6].
Fig. 6. Gain curves plotted against the a priori SNR é and the instantaneous SNR y — 1 for the MMSE STSA estimators: (a) Gy (Gaussian speech prior) defined by (15), (b) G, (Laplacian speech prior) defined by (22), (c) Gc (Gamma speech prior) defined by (27), and (d) the Ephraim and Malah solution Ggy (complex Gaussian speech prior), as seen in [(14)] [6].
Fig. 7. Gain curves comparison for the proposed MMSE STSA estimators for (a) € = —15 dB, (b) € = —5 GB, (c) € = 5 dB and (d) € = 15 GB. The solid, dashed and dotted lines correspond to Gy (Gaussian speech prior), G, (Laplacian speech prior) and Gg (Gamma speech prior), respectively. The corresponding Wiener filter solution given by (19) (Gaussian speech prior, linear filter), and the Ephraim and Malah solution [(14)] [6] Gew (complex Gaussian speech prior), are respectively plotted with dash-dotted and loosely dotted lines for comparison.
Fig. 7. Gain curves comparison for the proposed MMSE STSA estimators for (a) € = —15 dB, (b) € = —5 GB, (c) € = 5 dB and (d) € = 15 GB. The solid, dashed and dotted lines correspond to Gy (Gaussian speech prior), G, (Laplacian speech prior) and Gg (Gamma speech prior), respectively. The corresponding Wiener filter solution given by (19) (Gaussian speech prior, linear filter), and the Ephraim and Malah solution [(14)] [6] Gew (complex Gaussian speech prior), are respectively plotted with dash-dotted and loosely dotted lines for comparison.
Fig. 9. Gain curves for the proposed MMSE STSA estimators under speech presence uncertainty (SPU) for (a) € = —15 dB, (b) € = —5 dB, (c) € = 5 dB and (d) é = 15 GB, with q = 0.2. The solid, dashed and dotted lines correspond to Gj" (Gaussian speech prior) defined by (36), G}”" (Laplacian speech prior) defined by (37), and G2” (Gamma speech prior) defined by (39), respectively. The corresponding curves for the modified Wiener filter [11] (Gaussian speech prior, linear filter), and the Ephraim and Malah solution [(30)] [6] Gay ( (complex Gaussian speech prior), are respectively indicated with dash-dotted and loosely dotted line for reference.
Fig. 9. Gain curves for the proposed MMSE STSA estimators under speech presence uncertainty (SPU) for (a) € = —15 dB, (b) € = —5 dB, (c) € = 5 dB and (d) é = 15 GB, with q = 0.2. The solid, dashed and dotted lines correspond to Gj" (Gaussian speech prior) defined by (36), G}”" (Laplacian speech prior) defined by (37), and G2” (Gamma speech prior) defined by (39), respectively. The corresponding curves for the modified Wiener filter [11] (Gaussian speech prior, linear filter), and the Ephraim and Malah solution [(30)] [6] Gay ( (complex Gaussian speech prior), are respectively indicated with dash-dotted and loosely dotted line for reference.
Fig. 10. Performance comparison among various estimators tested using the oracle noise estimator (left column) and blind noise estimation given the noisy speech (righ column). Results are shown in terms of PESQ, STOI and Segmental SNR improvements and averaged over seven noise types (white noise, pink noise, speech noise, voice babbl noise, F-16 noise, car factory noise and car Volvo-340 noise).
Fig. 10. Performance comparison among various estimators tested using the oracle noise estimator (left column) and blind noise estimation given the noisy speech (righ column). Results are shown in terms of PESQ, STOI and Segmental SNR improvements and averaged over seven noise types (white noise, pink noise, speech noise, voice babbl noise, F-16 noise, car factory noise and car Volvo-340 noise).
Performance comparison, in terms of PESQ score gains, between various estimators tested using the nominated MMSE noise estimator.
Performance comparison, in terms of PESQ score gains, between various estimators tested using the nominated MMSE noise estimator.
Performance comparison, in terms of Segmental SNR gains, between various estimators tested using the nominated MMSE noise estimator.
Performance comparison, in terms of Segmental SNR gains, between various estimators tested using the nominated MMSE noise estimator.
Fig. 11. Performance comparison among various estimators with speech presence uncertainty (SPU) tested using the oracle noise estimator (left column) and blind nois¢ estimation given the noisy speech (right column). Results are shown in terms of PESQ, STO] and Segmental SNR improvements and averaged over seven noise types (white noise, pink noise, speech noise, voice babble noise, F-16 noise, car factory noise and car Volvo-340 noise).
Fig. 11. Performance comparison among various estimators with speech presence uncertainty (SPU) tested using the oracle noise estimator (left column) and blind nois¢ estimation given the noisy speech (right column). Results are shown in terms of PESQ, STO] and Segmental SNR improvements and averaged over seven noise types (white noise, pink noise, speech noise, voice babble noise, F-16 noise, car factory noise and car Volvo-340 noise).
Performance comparison, in terms of STOI score gains, between various estimators tested using the nominated MMSE noise estimator.
Performance comparison, in terms of STOI score gains, between various estimators tested using the nominated MMSE noise estimator.
Fig. 12. Spectrograms of (a) the clean sentence, (b) the sentence corrupted by non-stationary F-16 noise at O dB, and (c)-(j) enhanced speech produced by corresponding speech enhancement algorithm (see Table 1). The sentence 'Pitch the straw through the door of the stable’ (utterance MK62_09), was taken from the TSP speech database [47]. The nominated MMSE noise estimator introduced in Appendix D and in [35] were used for the DCT-based methods and DFT-based methods, respectively. The decision- directed approach [6] was used for the a priori SNR estimation.
Fig. 12. Spectrograms of (a) the clean sentence, (b) the sentence corrupted by non-stationary F-16 noise at O dB, and (c)-(j) enhanced speech produced by corresponding speech enhancement algorithm (see Table 1). The sentence 'Pitch the straw through the door of the stable’ (utterance MK62_09), was taken from the TSP speech database [47]. The nominated MMSE noise estimator introduced in Appendix D and in [35] were used for the DCT-based methods and DFT-based methods, respectively. The decision- directed approach [6] was used for the a priori SNR estimation.
Fig. 13. Spectrograms of (a) the clean sentence, (b) the sentence corrupted by voice babble noise at 0 dB, and (c)-(j) enhanced speech produced by corresponding speech enhancement algorithm (see Table 1). The sentence ‘The dune rose from the edge of the water’ (utterance FBO7_09), was taken from the TSP speech database [47]. The nominated MMSE noise estimator introduced in Appendix D and in [35] were used for the DCT-based methods and DFT-based methods, respectively. The decision-directed approach [6] was used for the a priori SNR estimation.
Fig. 13. Spectrograms of (a) the clean sentence, (b) the sentence corrupted by voice babble noise at 0 dB, and (c)-(j) enhanced speech produced by corresponding speech enhancement algorithm (see Table 1). The sentence ‘The dune rose from the edge of the water’ (utterance FBO7_09), was taken from the TSP speech database [47]. The nominated MMSE noise estimator introduced in Appendix D and in [35] were used for the DCT-based methods and DFT-based methods, respectively. The decision-directed approach [6] was used for the a priori SNR estimation.
Fig. 14. The mean subjective preference score (%) comparison for each speech enhancement method. The male utterance (MK62_09) corrupted with 5 dB non-stationary F-" noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Fig. 14. The mean subjective preference score (%) comparison for each speech enhancement method. The male utterance (MK62_09) corrupted with 5 dB non-stationary F-" noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Fig. 15. The mean subjective preference score (%) comparison for each speech enhancement method. The female utterance (FBO7_09) corrupted with 5 dB voice babble noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Fig. 15. The mean subjective preference score (%) comparison for each speech enhancement method. The female utterance (FBO7_09) corrupted with 5 dB voice babble noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Fig. 16. Performance comparison between the state of the art phase-aware estimators (i.e., ADP [51], AUP [27], and MAUP [28]) and the propose estimators [i.e., Gy (15), G, (22), and G¢ (27)] using blind a prior SNR and noise PSD estimation. The clean speech and noisy (unprocessed) speech are also included as the upper bound and lower bound of the performance, respectively. Results are shown in terms of conventional (i.e., PESQ, STOI and Segmental SNR) and phase-aware (i.e., PD, UnRMSE, and UnHPSNR) instrumental metrics. Scores of the metrics were averaged over seven noise types (white noise, pink noise, speech noise, voice babble noise, F-16 noise, car factory noise and car Volvo-340 noise).
Fig. 16. Performance comparison between the state of the art phase-aware estimators (i.e., ADP [51], AUP [27], and MAUP [28]) and the propose estimators [i.e., Gy (15), G, (22), and G¢ (27)] using blind a prior SNR and noise PSD estimation. The clean speech and noisy (unprocessed) speech are also included as the upper bound and lower bound of the performance, respectively. Results are shown in terms of conventional (i.e., PESQ, STOI and Segmental SNR) and phase-aware (i.e., PD, UnRMSE, and UnHPSNR) instrumental metrics. Scores of the metrics were averaged over seven noise types (white noise, pink noise, speech noise, voice babble noise, F-16 noise, car factory noise and car Volvo-340 noise).
Fig. 17. The mean subjective preference score (%) comparison for each speech enhancement method. The female utterance (FF36_08) corrupted with 5 dB voice babble noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Fig. 17. The mean subjective preference score (%) comparison for each speech enhancement method. The female utterance (FF36_08) corrupted with 5 dB voice babble noise was used for the subjective tests. The error bars indicated the standard deviation of the scores.
Using the expression for the parabolic cylinder function from (26) and the relations [Th.9.212.2,9.212.3][38] yields Appendix D. MMSE-based Noise Power Estimation
Using the expression for the parabolic cylinder function from (26) and the relations [Th.9.212.2,9.212.3][38] yields Appendix D. MMSE-based Noise Power Estimation
Noise estimator comparisons. p(Hi|Y) ~ 1, the noise update will cease and the noise estimate will remain the same as the previous frame’s estimate. Following the preceding computation of E{|DP\y}, the long-term noise PSD was then obtained via recursive smoothing with 8 = 0.95 p(Hi|Y) ~ 1, the noise update will cease and the noise estimate will remain the same as the previous frame’s estimate. Following the Cc a Oe tor, E{|DPIY, Ho}, with the periodogram of the noisy speech |Y|?. Furthermore, P(|Y||Ho) has the folded-normal PDF [37] Table 5 preceding computation of Ey IDI"IY +, the long-term noise PSD was
Noise estimator comparisons. p(Hi|Y) ~ 1, the noise update will cease and the noise estimate will remain the same as the previous frame’s estimate. Following the preceding computation of E{|DP\y}, the long-term noise PSD was then obtained via recursive smoothing with 8 = 0.95 p(Hi|Y) ~ 1, the noise update will cease and the noise estimate will remain the same as the previous frame’s estimate. Following the Cc a Oe tor, E{|DPIY, Ho}, with the periodogram of the noisy speech |Y|?. Furthermore, P(|Y||Ho) has the folded-normal PDF [37] Table 5 preceding computation of Ey IDI"IY +, the long-term noise PSD was
Fig. 18. The total probability of error as a function of Sun. The optimal &,, is found by minimizing the total probability of error when ¢ is uniformly distributed between €,., = 0 and €,, = 100,
Fig. 18. The total probability of error as a function of Sun. The optimal &,, is found by minimizing the total probability of error when ¢ is uniformly distributed between €,., = 0 and €,, = 100,
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Speech enhancementSingle-Channel Speech Enhancement
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