The mean squared error (MSE) is a ubiquitous loss function for speech enhancement, but its problem is that the error cannot reflect the auditory perception quality. This is because MSE causes models to over-emphasize low-frequency components which has high energy, leading to the inadequate modeling of perceptually important high-frequency information. To overcome this limitation, we propose a perceptually-weighted loss function grounded in psychoacoustic principles. Specifically, it leverages equal-loudness contours to assign frequency-dependent weights to the reconstruction error, thereby penalizing deviations in a way aligning with human auditory sensitivity. The proposed loss is model-agnostic and flexible, demonstrating strong generality. Experiments on the VoiceBank+DEMAND dataset show that replacing MSE with our loss in a GTCRN model elevates the WB-PESQ score from 2.17 to 2.93-a significant improvement in perceptual quality.
Figures & tables
Figure 1: Overview of the Loud-loss computation pipeline.
Freq
SPL
Freq
SPL
Freq
SPL
Freq
SPL
(Hz)
(dB)
(Hz)
(dB)
(Hz)
(dB)
(Hz)
(dB)
20
99.85
25
93.94
31.5
88.17
40
82.63
50
77.78
63
73.08
80
68.48
100
64.37
125
60.59
160
56.70
200
53.41
250
50.40
315
47.58
400
44.98
500
43.05
630
41.34
800
40.06
1000
40.01
1250
41.82
1600
42.51
Table 1: Required SPL (dB) versus frequency (Hz) for the 40-phon equal-loudness contour.
Exp. ID
Models
Type
Loss
WB-PESQ
NB-PESQ
ESTOI
-
Unprocessed
-
-
1.97
2.88
0.787
1
GTCRN †
Mapping
MSE
2.17
3.04
0.812
2
GTCRN † + PCS
Mapping
MSE
2.48
3.20
0.807
3
GTCRN †
Mapping
Loud-loss
2.93
3.51
0.836
4
GTCRN ‡
Masking
MSE
2.57
3.24
0.824
5
GTCRN ‡
Masking
Loud-loss
2.92
3.50
0.841
Table 2: Objective evaluation results on the VoiceBank+DEMAND test set. Boldface indicates the best score in each column. † denotes magnitude mapping-based methods, while ‡ denotes masking-based methods.
Figure 2: Comparison of enhanced speech spectrograms generated using different loss functions.
Exp. ID
Description
WB-PESQ
3
Baseline (Loud-loss)
2.93
Analysis of Sub-band Splitting
11
w/o Sub-band Overlap
2.81
12
Uniform Band Split
2.40
13
Per-bin Weighting (no bands)
2.56
Analysis of Weighting Scheme
Table 3: Ablation study of the Loud-loss on the GTCRN † model. "Baseline" refers to our full proposed method (Exp. 3).
Loss
DNSMOS
NISQA
P.808
SIG
BAK
OVRL
MOS
Noise
Color
Disc.
Loud.
MSE
3.0477
2.9139
3.0105
2.3416
2.3468
2.0555
2.6022
3.0961
3.0108
PFPL
3.2226
2.9757
3.4343
2.5276
2.4191
2.8315
2.7386
3.1316
3.1564
MetricGAN
3.2266
2.9424
3.4958
2.5285
2.5918
2.9450
2.7597
3.5369
3.0876
Loud-loss
3.2272
2.8972
3.6656
2.5500
2.5189
3.0390
2.7500
3.4316
3.1426
Table 4: Evaluation on the DNS3 blind test set.
Method
Extra net
Params (M)
Time (ms)
Rel. to MSE
Memory (MB)
FLOPs (G)
MSE
None
0.028
18.43±3.14
1.00×
313.6
2.96
PFPL
Frozen wav2vec
32.565
56.65±4.88
3.07×
871.1
296.14
MetricGAN
Discriminator
0.209
162.92±14.04
8.84×
329.8
7.67
Loud-loss
None
0.028
19.38±2.88
1.05×
313.6
2.96
Table 5: Training-cost comparison with other perceptually motivated methods.
Speech enhancement improves intelligibility and listening quality by suppressing noise, reverberation, and competing speakers in recorded or live audio.
Contemporary deep speech enhancement (SE) models are often trained with specific auxiliary terms in the loss function as a way to improve their performance in terms of perceptual metrics. Nevertheless, a higher score on a perceptual metric does not necessarily correlate with an improved listening experience. Through objective and subjective experiments, we assess the performance of SE models trained with two different types of auxiliary PESQ loss terms. The numerical evaluation on a suite of standard metrics suggests that, while models optimized for PESQ naturally obtain higher PESQ scores in the test set, for most other metrics the scores do not significantly change. In some cases, the PESQ loss even results in worse PESQ scores on mismatched data. A formal listening experiment reveals that the models without a PESQ loss were generally preferred over models that include it, across all settings. Finally, we analyze the relative importance of PESQ in the composite metrics CSIG, CBAK and COVL, and find that PESQ dominates all of them. Our study highlights the perils of over-reliance on PESQ and stresses the importance of a complete evaluation procedure for SE.
Danilo de Oliveira, Tal Peer, Maurício do V. M. da Costa +1
Speech enhancement language models achieve strong results when trained on discrete audio tokens, but their optimization relies on token-level cross-entropy rather than the perceptual metrics used for evaluation. We introduce a post-training stage for autoregressive speech enhancement language models using Group Sequence Policy Optimization (GSPO) with multi-metric perceptual rewards. Our method directly optimizes non-differentiable quality metrics (DNSMOS, WER, and UTMOS) as reward signals, without learned surrogates or offline preference pairs. Applied to two autoregressive base models, UniSE and GenSE, our approach achieves state-of-the-art results on the DNS2020 benchmark. A human evaluation ablation further shows that the composite multi-metric reward is preferred over any single-metric variant, confirming that multi-reward optimization avoids the reward hacking observed with single-metric training.
Frédéric Berdoz, Luca A. Lanzendörfer, Antonis Asonitis +1
Conventional training losses for speech enhancement based on the signal-to-distortion ratio (SDR) treat all time-frequency (TF) regions uniformly, overlooking the fine-grained spectral cues that are relevant to specific phoneme intelligibility. We propose a TF weighting framework that modulates the SDR objective based on local speech presence, speech-to-interference ratio (SIR), and spectral flux. By integrating these factors into a differentiable objective, the framework emphasizes TF bins with high speech-noise competition while also accounting for transient cues such as consonant bursts. Experimental results show that our approach improves objective frequency-weighted enhancement metrics, as well as phoneme recognition accuracy, particularly for consonants. Spectral analysis shows better reconstruction of mid-frequency structures at less adverse SIR.
Nasser-Eddine Monir, Paul Magron, Romain Serizel
Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France