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10th Convention of the European Acoustics Association
Turin, Italy • 11th – 15th September 2023 • Politecnico di Torino
EXPLORING THE IMPACT OF TRANSFER LEARNING
ON GAN-BASED HRTF UPSAMPLING
Aidan O. T. Hogg He Liu Mads Jenkins Lorenzo Picinali
Audio Experience Design Team, Dyson School of Design Engineering
Imperial College London, UK
ABSTRACT
Individualised head-related transfer functions (HRTFs)
are essential for creating realistic virtual reality (VR) and
augmented reality (AR) environments and interactions.
Performing acoustic measurements is the most accurate
way to capture these individualised HRTFs. However,
one of the main challenges is acoustically capturing high-
quality HRTFs without the need for expensive equipment
and a lab-controlled setting. To make these measurements
more feasible on a large scale, HRTF upsampling has been
exploited in the past, where a high-resolution HRTF is
created from a low-resolution measurement. However, as
the world shifts to more data-driven methods, upsampling
HRTFs using machine learning (ML) has become more
prevalent. The main limitation is the lack of HRTF data
available for model training. This paper explores the
use of transfer learning (TL) on a new synthetic HRTF
dataset generated from three-dimensional (3D) meshes
using a parametric pinna model and the performance
improvements that can be achieved. The performance
is also compared against using a small acoustically
measured dataset for TL, with the aim to start answering
the question: ‘Is it better to have more data, or is it better
for the data to be of higher quality?’.
Keywords: transfer learning, generative adversarial
network, head-related transfer function, super-resolution,
upsampling.
*Corresponding author: aidan@aidanhogg.uk.
Copyright: ©2023 Aidan O. T. Hogg et al. This is an
open-access article distributed under the terms of the Creative
Commons Attribution 3.0 Unported License, which permits
unrestricted use, distribution, and reproduction in any medium,
provided the original author and source are credited.
1. INTRODUCTION
We live in a world where communication is vital, and
this could not be more evident when it comes to online
interactions. We all desire seamless remote connectivity,
whether it be in an online meeting or the latest VR
experience. The ability to create realistic, immersive
audio scenarios is needed to achieve this. Immersive audio
is what we experience in everyday life; some sounds are
close, some are far away, some are moving, and all come
from different directions. In most real-life situations, the
lack of immersive audio leads to frustration often felt
when communicating remotely [1].
One way to achieve high realism in immersive audio
is to exploit our two ears and generate realistic sounds at
these two sensors. The question is how sounds that mimic
real-world 3D audio can accurately be created [2] and,
more specifically, how this can be adapted for individual
listeners. This individualisation has resulted in a large
amount of research focusing on HRTFs, which capture
the interaural (i.e. differences heard between the listener’s
two ears) and monaural localisation cues [3].
It has been shown in the past that many approaches
can be deployed for this HRTF individualisation task, and
an overview of some of the most common methods can be
found in [4]. However, taking an acoustic measurement
[5] is still considered to be the gold standard among these
different approaches. The downside is the time it takes
and the expensive custom setup required. To overcome
these issues and to make the method scalable, spatial up-
sampling methods have been proposed in the past that
can generate spatial high-resolution HRTFs from low-
resolution ones [6]. This process is commonly referred to
as HRTF upsampling and can be achieved using various
approaches.
The main aim of this paper is to investigate the use
10th Convention of the European Acoustics Association
Turin, Italy • 11th – 15th September 2023 • Politecnico di Torino
of TL on an ML approach that uses a super-resolution
generative adversarial network (SRGAN) to tackle the
HRTF up-sampling problem. The paper builds on a pilot
study that was undertaken in [7] and the SRGAN approach
of [8] and [9]. The advantage of ML approaches over
traditional upsampling is that it is able to recreate the
missing information in the sparse measurements using
the knowledge learnt from a training set that contains
many high-resolution HRTFs. The main drawback,
currently, is the limited amount of acoustically measured
HRTF data available for training. A common solution
to this problem of limited data is TL, which has been
shown to be successful in many domains, including
image recognition, natural language processing (NLP)
and speech recognition [10–12]. In [13], TL was used
in conjunction with GANs for image reconstruction of
under-sampled magnetic resonance imaging (MRI) data.
[14] also showed the benefits of TL when a GAN used for
image generation was pre-trained with ImageNet. There
is no standard implementation of TL; [15] described over
20 different strategies. A common approach is to train
the entire network with pre-training data and then retrain
the entire network with task-training data, which will be
exploited in this work. This paper will present the results
of TL using a new synthetic HRTF dataset generated
from 3D meshes using a parametric pinna model and the
performance improvements that can be obtained.
2. METHOD
In the past, SRGANs have performed well on the task
of up-sampling images. However, when applying this
approach to HRTFs up-sampling, the main challenge is
that the data occupies an extra dimension in physical space
where it is not uniformly distributed. One way to solve
this problem is to modify the network to handle this non-
uniformly distributed HRTF data, such as graph neural
networks (GNNs) [16]. However, in this work, a pre-
processing step is used to convert the spherical HRTF data
into a form that all of the image upsampling literature can
exploit.
2.1 Pre-processing
This pre-processing consists of two main steps 1) the
spherical HRTF data is projected onto a two-dimensional
(2D) surface using a gnomonic equiangular projection to
remove the extra dimension. 2) barycentric interpolation
[17] is utilised to shift the irregularly spaced impulse
responses (IRs) onto an evenly spaced Cartesian grid.
A detailed description of this approach is given in [8].
One of the big advantages of this pre-processing is that
it becomes possible for the SRGAN network to exploit
many different HRTF datasets for training, which is
essential for TL. This is true even when two datasets
contain spatially very different measurements because the
points will all be mapped onto the same Cartesian grid.
2.2 GAN Architecture
A GAN architecture, similar to that of [18], is exploited
where the generator network G, in this case, aims
to generate high-resolution HRTFs from low-resolution
HRTF inputs. On the other hand, the discriminator
network Daims to discriminate whether a HRTF is real
or generated by the network G. The loss function used
is a weighted sum of the content loss, which compares
the output of Gusing the log-spectral distortion (LSD) to
the high-resolution ground truth, with an adversarial loss,
which measures how frequently Gsuccessfully fools D.
2.3 Transfer Learning
This paper aims to explore improvements that can be
achieved from the use of TL and attempts to answer the
question: ‘When it comes to TL for HRTF upsampling, is
it better to have more data, or is it better for the data to be
more realistic?’. To achieve this, TL is employed by first
pre-training the SRGAN before retraining on the HRTF
task data. A comparison of two types of pre-training data
is presented: acoustically measured data from a different
dataset to the task data and a newly created synthetic
dataset. Due to the synthetic dataset being much larger
than the acoustically measured dataset, this should help
in beginning to address the question of whether quality or
quantity is more important.
2.4 Post-processing
The full HRTFs were reconstructed after upsampling
using a minimum-phase approximation and a simple ITD
model to perform this perceptual evaluation.
3. TRAINING
The high-resolution 1280 target is generated by process-
ing the ARI HRTF dataset (which contains 1550 posi-
tions for each listener, see Section 4.2.1) using the pre-
processing described in Section 2.1.
To obtain the low-resolution HRTFs from their high-
resolution counterparts, the HRTFs are downsampled
10th Convention of the European Acoustics Association
Turin, Italy • 11th – 15th September 2023 • Politecnico di Torino
Table 1.A comparison of the mean log-spectral
distortion (LSD) and standard deviation (SD) error across
all source positions in the ARI dataset for different
upsampling factors where the results are given in decibels
[dB]. The ‘best’ performance of each upsampling factor
has been highlighted.
Method Upsample Factor (No. original →upsampled) [dB]
320 →1280 80 →1280 20 →1280 5 →1280
SRGAN (No TL) 3.28 (0.13) 4.86 (0.24) 4.99 (0.27) 5.30 (0.35)
TL (Synthetic) 3.02 (0.15) 4.07 (0.19) 4.75 (0.28) 5.16 (0.39)
TL (SONICOM) 3.05 (0.14) 4.21 (0.17) 4.79 (0.25) 5.39 (0.33)
Baseline 2.50 (0.20) 3.71 (0.22) 5.18 (0.23) 7.30 (0.33)
320 )1280 80 )1280 20 )1280 5 )1280
Upsample Factor
(No. of original nodes )No. of upsampled nodes)
2
4
6
8
ARI
LSD error [dB]
SRGAN (No TL)
TL (Synthetic)
TL (SONICOM)
Baseline
Figure 1.Log-spectral distortion (LSD) evaluation.
using the torch.nn.functional.interpolate
function. To evaluate the performance of the GAN, results
from four different downsampling rates are given, where
the number of original positions kept is 320, 80, 20 and
5. The high-resolution HRTF target of 1280 positions
was selected as it is comparable to the 1550 positions
measured in the ARI HRTF dataset.
It should also be noted that while HRTFs possess both
magnitude and phase components, only the magnitude
component is used as an input to the SRGAN. The
model was trained using the Adam optimiser [19], with
hyperparameter values of β1= 0.9and β2= 0.999.
The learning rates for the generator, G, and discriminator,
D, networks were set as 2.0×10−4and 1.5×10−6,
respectively. In training, Dand Gwere alternately
updated with different frequencies, with Dbeing updated
four times for every Gupdate. Gcontains 8 residual
blocks and 512 hidden features. This model was
implemented using a PyTorch framework and trained on
an NVIDIA Quadro RTX 6000 graphics processing unit
(GPU).
4. RESULTS
The code to reproduce these results is provided in [9].
4.1 Experimental Setup
Results are given for the ARI dataset; the SONICOM
dataset is used for TL and represents an acoustically
measured dataset for comparison. These results are
compared against using the SONICOM Synthetic dataset
for TL as well as the performance without the use of
TL. Barycentric interpolation, as implemented in [17], is
also used as a baseline as it is one of the most common
methods for HRTF upsampling.
4.2 Experimental Data
4.2.1 SONICOM and ARI
The SONICOM dataset [5, 20] is a publicly-released
HRTF dataset which aims at facilitating reproducible
research in the spatial acoustics and immersive audio
domain by including in a single database HRTFs
measured from an increasingly large number of subjects
(200 subjects were used in this work). The ARI
HRTF database [21], on the other hand, contains HRTF
measurements on 221 subjects, making it one of the
largest measured HRTF datasets available.
4.2.2 SONICOM Synthetic
This newly created dataset was generated from 3D meshes
using the boundary element method (BEM) [22] and the
open-source tool Mesh2HRTF [23]. The parametric pinna
model (PPM) [24] was used to generate these meshes. The
9 control bone parameters and 18 shape key parameters
(which customised 134 overall dimensions) used in the
PPM are selected randomly from a normal distribution
where the mean and standard deviation are chosen by
taking the average parameters from 15 pinna models. To
introduce differences between the left and right ear, the
left ear is first generated, and then for each parameter, a
maximum of 20% difference of the parameter range is
added, with the amount chosen being randomly selected
from a normal distribution. The left and right ear meshes
are then stitched onto a dummy head [25]. To speed up
the computation, the meshes (containing approximately
63,000 triangles) are downscaled to between 16,000
10th Convention of the European Acoustics Association
Turin, Italy • 11th – 15th September 2023 • Politecnico di Torino
−50
0
50
ARI
Polar ACC error [◦]
SRGAN (No TL)
TL (Synthetic)
TL (SONICOM)
Baseline
Target
0
20
40
ARI
Quadrant error [%]
320 )1280 80 )1280 20 )1280 5 )1280
Upsample Factor
(No. of original nodes )No. of upsampled nodes)
30
40
ARI
Polar RMS error [◦]
Figure 2.Perceptual evaluation.
to 20,000 triangles using the mesh grading plugin on
OpenFlipper [26]. This mesh grading used the fourth-
order COSalpha grading function with a minimum and
maximum global target edge length of 0.0015 m and
0.01 m, respectively.
Finally, the graded meshes are passed as the input
into Mesh2HRTF, where the output frequency range of
the HRTF was set to 100 - 16,000 Hz (128 samples), the
speed of sound was set to 346.18 (m/s), and the density
of air was set to 1.1839 (kg/m3). The magnitude of the
generated synthetic HRTF data was then scaled to match
the ARI and SONICOM datasets more closely.
4.3 Comparative Evalulation
4.3.1 Log-spectral distortion (LSD) evalulation
The LSD metric is defined as
LSD =1
NPN
n=1 s1
WPW
w=1 20 log10
|HHR(fw, xn)|
|HUS(fw, xn)|2
,(1)
Table 2.The mean and standard deviation (SD) values
of the perceptual evaluation across the subjects in the
ARI test set for the different upsampling factors. The
‘best’ performance of each upsampling factor has been
highlighted.
(a) Polar accuracy error comparison where the results are given
in degrees [◦].
Method Upsample Factor (No. original →upsampled) [◦]
320 →1280 80 →1280 20 →1280 5 →1280
SRGAN (No TL) 0.46 (4.50) 4.38 (6.63) 1.04 (8.46) -1.95 (8.71)
TL (Synthetic) -0.17 (4.30) 3.48 (4.55) -0.58 (7.18) 3.05 (8.39)
TL (SONICOM) 0.60 (4.11) 0.36 (5.42) 0.50 (7.28) 3.38 (7.28)
Baseline 1.17 (3.84) 1.57 (4.32) 2.22 (8.36) -2.54 (23.84)
Target 0.93 (3.72)
(b) Quadrant error comparison where the results are given as a
percentage [%].
Method Upsample Factor (No. original →upsampled) [%]
320 →1280 80 →1280 20 →1280 5 →1280
SRGAN (No TL) 8.33 (2.84) 9.96 (3.34) 12.39 (3.79) 12.84 (3.71)
TL (Synthetic) 8.59 (2.72) 9.01 (2.90) 12.35 (3.19) 12.67 (4.09)
TL (SONICOM) 8.30 (2.68) 7.78 (2.42) 12.29 (3.58) 14.15 (4.44)
Baseline 8.50 (2.68) 9.15 (2.73) 13.79 (3.76) 24.65 (7.28)
Target 8.03 (2.65)
(c) Polar root mean square (RMS) error comparison where the
results are given in degrees [◦].
Method Upsample Factor (No. original →upsampled) [◦]
320 →1280 80 →1280 20 →1280 5 →1280
SRGAN (No TL) 32.97 (1.83) 35.46 (1.77) 35.89 (1.70) 36.51 (1.64)
TL (Synthetic) 32.84 (1.83) 33.75 (1.87) 35.27 (1.79) 35.93 (1.65)
TL (SONICOM) 32.48 (1.89) 33.64 (1.97) 35.69 (1.58) 36.66 (1.54)
Baseline 32.61 (1.70) 33.75 (1.68) 38.24 (1.36) 41.79 (1.22)
Target 32.26 (1.73)
where |HHR(fw, xn)|and |HUS (fw, xn)|represent the
magnitude responses of the high-resolution and up-
sampled HRTF sets, Wis the number of frequency bins
in the HRTF, Nis the number of locations, fwis the
frequency, and xnis the location. In these results, the
LSD is calculated for every measurement source position
and then averaged over all the source positions.
Table 1 and Fig. 1 show the average results for
the LSD evaluation over the ARI test set. In Fig. 1,
the TL approaches show clear benefits over standard
training. The most interesting observation, however,
10th Convention of the European Acoustics Association
Turin, Italy • 11th – 15th September 2023 • Politecnico di Torino
is that using the SONICOM Synthetic dataset of 1000
subjects for TL slightly outperforms using the acoustically
measured SONICOM dataset of 200 subjects. This result
is potentially highly advantageous as synthetic HRTF data
is much quicker and cheaper to generate than undertaking
costly acoustic measurements.
4.3.2 Model-based perceptual evaluation
To compare the localisation performance, a Bayesian
model [27] for predicting human localisation performance
was also used. Unlike the LSD metric, this model
can evaluate the different approaches based on attributes
that matter to human perception. This is important as
not all errors in the LSD impact human localisation
performance in the same way. To perform an effective
comparison, the results for the original high-resolution
measured HRTFs are provided as the ‘Target’ results.
These ‘Target’ results are the best performance that can
be achieved as it effectively compares the localisation
performance of the original high-resolution HRTF with
itself. Therefore the proposed method and the baseline
need to be benchmarked against the ‘Target’ performance.
Similarly to the results shown for the LSD evaluation,
Table 2 and Fig. 2 show the positive impact of using
TL for HRTF upsampling. The TL approach using
the acoustically measured data (SONICOM) can even
outperform the barycentric baseline at every upsampling
factor. It should also be noted that TL with both
synthetic and acoustically measured data leads to similar
performance gains, with the acoustically measured only
slightly outperforming synthetic data in a few instances.
This result could be explained considering the fact that
the training uses more realistic data and should therefore
lead to better perceptual performance but not necessarily
a better performance in terms of LSD, which is the case
here.
5. CONCLUSION
In this paper, it has been shown that SRGAN HRTF
upsampling can exploit the use of TL to improve
performance. Furthermore, it has also been shown
that synthetic data works well for TL, sometimes
outperforming acoustically measured data.
6. ACKNOWLEDGMENTS
This research is supported by the SONICOM project (EU
Horizon 2020 RIA grant agreement ID: 101017743).
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