Loud-loss: A Perceptually Motivated Loss Function for Speech Enhancement Based on Equal-Loudness Contours

Zixuan Li; Xueliang Zhang; Changjiang Zhao; Shuai Gao; Lei Miao; Zhipeng Yan; Ying Sun; Chong Zhu

cs.SDNov 8, 2025

Loud-loss: A Perceptually Motivated Loss Function for Speech Enhancement Based on Equal-Loudness Contours

Authors: Zixuan Li, Xueliang Zhang, Changjiang Zhao, Shuai Gao, Lei Miao, Zhipeng Yan, Ying Sun, Chong Zhu

Organizations: College of Computer Science, Inner Mongolia University, China · Lenovo, China

Abstract

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.

Analysis of Sub-band Splitting
Exp. ID	Description	WB-PESQ
3	Baseline (Loud-loss)	2.93
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
Loss	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	$18.43{\pm}3.14$	$1.00\times$	313.6	2.96
PFPL	Frozen wav2vec	32.565	$56.65{\pm}4.88$	$3.07\times$	871.1	296.14
MetricGAN	Discriminator	0.209	$162.92{\pm}14.04$	$8.84\times$	329.8	7.67
Loud-loss	None	0.028	$19.38{\pm}2.88$	$1.05\times$	313.6	2.96

Table 5: Training-cost comparison with other perceptually motivated methods.

Speech Enhancement

Speech enhancement improves intelligibility and listening quality by suppressing noise, reverberation, and competing speakers in recorded or live audio.

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Perceptual Quality Loss or Loss of Perceptual Quality?

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Open paper AskPDF arXiv

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.

Abstract

Speech Enhancement

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