Regularization for Partial Multichannel Equalization for Speech Dereverberation
A. Acoustic System and Performance Measures
- Single source 2-microphone scenario
- Reverberation time T60 = 550 ms
- Sampling frequency fs = 16 kHz
- RIR length Lh = 4400
- Reshaping filter length Lg = 4399
- Delay (in number of samples) τ = 0
- Desired window lengths Ld: 10 ms, 20 ms, 30 ms, 40 ms, 50 ms
- Performance measures:
- EDC
- PESQ
B. Optimal Regularization in the Presence of Channel Estimation Errors
Simulation 1: Normalized channel mismatch Em = -33 dB
CS1 is the CS eigenvector leading to the minimum l2-norm estimated EIR
CS2 is the CS eigenvector leading to the maximum PESQ score
| Ld [ms] | MINT | Regularized MINT | RMCLS | Regularized RMCLS | CS1 | CS2 | Regularized CS | P-MINT | Regularized P-MINT | Reference Signal |
|---|---|---|---|---|---|---|---|---|---|---|
| 10 | ||||||||||
| 20 | ||||||||||
| 30 | ||||||||||
| 40 | ||||||||||
| 50 |
Simulation 2: Normalized channel mismatch Em = -15 dB
CS1 is the CS eigenvector leading to the minimum l2-norm estimated EIR
CS2 is the CS eigenvector leading to the maximum PESQ score
| Ld [ms] | MINT | Regularized MINT | RMCLS | Regularized RMCLS | CS1 | CS2 | Regularized CS | P-MINT | Regularized P-MINT | Reference Signal |
|---|---|---|---|---|---|---|---|---|---|---|
| 10 | ||||||||||
| 20 | ||||||||||
| 30 | ||||||||||
| 40 | ||||||||||
| 50 |
C. Automatic Regularization in the Presence of Channel Estimation Errors
Normalized channel mismatch Em = -15 dB and several desired window lengths Ld
| Ld [ms] | Optimal Regularization | Automatic Regularization | Reference Signal |
|---|---|---|---|
| 10 | |||
| 20 | |||
| 30 | |||
| 40 | |||
| 50 |
Several normalized channel mismatches Em and desired window length Ld = 50 ms
Sound samples for reverberation time T60 = 550 ms
| Em [dB] | Optimal regularization | Automatic regularization | Reference Signal |
|---|---|---|---|
| -33 | |||
| -30 | |||
| -27 | |||
| -24 | |||
| -21 | |||
| -18 | |||
| -15 |
D. Robustness in the Presence of Channel Estimation Errors and Additive Noise
Input broadband SNR = 15 dB, normalized channel mismatch Em = -15 dB
| Ld [ms] | P-MINT | Automatic Regularized P-MINT | Reference Signal |
|---|---|---|---|
| 10 | |||
| 20 | |||
| 30 | |||
| 40 | |||
| 50 |
SNR improvement [dB]
| Ld [ms] | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| P-MINT | -11.24 | -23.11 | -25.20 | -31.22 | -19.59 |
| Automatic Regularized P-MINT | -3.22 | 4.39 | 2.89 | 0.39 | 2.14 |
PESQ score
| Ld [ms] | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| P-MINT | 1.65 | 1.83 | 1.78 | 2.03 | 2.29 |
| Automatic Regularized P-MINT | 2.25 | 2.60 | 2.79 | 2.81 | 3.07 |
| y1(n) | 1.99 | 2.11 | 2.27 | 2.39 | 2.52 |