HRIR-Former: Grid-Free Time-Domain Reconstruction of Head-Related Impulse Responses with a Spatially Encoded Transformer

Shaoheng Xu; Chunyi Sun; Jihui Zhang; Amy Bastine; Prasanga N. Samarasinghe; Thushara D. Abhayapala; Hongdong Li

eess.ASMar 30, 2026

HRIR-Former: Grid-Free Time-Domain Reconstruction of Head-Related Impulse Responses with a Spatially Encoded Transformer

Authors: Shaoheng Xu, Chunyi Sun, Jihui Zhang, Amy Bastine, Prasanga N. Samarasinghe, Thushara D. Abhayapala, Hongdong Li

Organizations: The Australian National University, Australia · The University of Queensland, Australia

Abstract

Individualized head-related impulse responses (HRIRs) enable binaural rendering, but dense per-listener measurements are costly. We address HRIR spatial up-sampling from sparse per-listener measurements: given a few measured HRIRs for a listener, predict HRIRs at unmeasured target directions. Prior learning methods often work in the frequency domain, rely on minimum-phase assumptions or separate timing models, and use a fixed direction grid, which can degrade temporal fidelity and spatial continuity. We propose HRIR-Former, a time-domain, grid-free binaural Transformer for reconstructing HRIRs at arbitrary directions from sparse inputs. It uses sinusoidal spatial features, a Conv1D refinement module, and auxiliary interaural time difference (ITD) and interaural level difference (ILD) heads. On SONICOM, it improves normalized mean squared error (NMSE), cosine distance, and ITD/ILD errors over prior methods; ablations validate modules and show minimum-phase preprocessing is unnecessary.

Figures & tables

Figure 1: Illustration of HRIR spatial up-sampling: estimating HRIRs at unmeasured target directions (white) from a sparse set of measured directions (red).

Figure 2: Overview of the proposed HRIR-Former pipeline. Known HRIRs are projected into a latent space using an MLP-based signal encoder, while geometric embeddings derived from direction coordinates are independently projected and added to the signal features. The resulting tokens are processed jointly by a Transformer encoder to capture global spatial dependencies across measured and target directions. A shared MLP decoder maps contextual features to full-length binaural HRIRs for all directions, followed by masked fusion to preserve measured responses and a lightweight Conv1D for temporal refinement.

Method	$M=3$		$M=5$		$M=19$		$M=100$
Method	ITD-E ( $\mu$ s) $\downarrow$	ILD-E (dB) $\downarrow$	ITD-E ( $\mu$ s) $\downarrow$	ILD-E (dB) $\downarrow$	ITD-E ( $\mu$ s) $\downarrow$	ILD-E (dB) $\downarrow$	ITD-E ( $\mu$ s) $\downarrow$	ILD-E (dB) $\downarrow$
HRIR-Former (Proposed)	18.5	1.14	16.4	1.10	15.4	0.95	10.6	0.70
Nbr [ 35 ]	274.2	7.6	154.2	4.8	108.3	3.0	44.0	1.4
HRTF-Sel-ITD [ 35 ]	26.3	1.4	24.5	1.5	23.2	1.6	20.0	1.4
HRTF-Sel-LSD [ 35 ]	37.5	1.5	35.7	1.4	37.4	1.5	31.4	1.3
NF-CbC [ 45 ]	22.1	1.5	20.7	2.0	14.8	1.8	11.8	1.7

Table 1: ITD-E (

\mu

s) and ILD-E (dB) under different measurement sparsity levels

M

on SONICOM. Bold indicates the best result per column. Baseline results are taken from [ 35 ] .

Metric	$M{=}3$	$M{=}5$	$M{=}19$	$M{=}100$
NMSE (dB) $\downarrow$	-6.90	-7.35	-8.24	-10.20
CD $\downarrow$	0.233	0.210	0.163	0.102

Table 2: NMSE and CD of HRIR-Former under different measurement sparsity levels

M

Figure 3: Left-ear HRIR reconstruction for subject P0187 at

(\phi,\theta,r)=(90^{\circ},20^{\circ},1.5~\mathrm{m})

under

M=19

: estimated HRIR (dashed) versus ground-truth HRIR (solid). Angular distance to the nearest measured direction:

35.2^{\circ}

Figure 4: Stacked binaural HRIRs for subject P0187 under $M=19$ over 793 directions (each column: one direction; left/right ears concatenated along time). Ground truth (left) and estimation (right).

Variant	NMSE (dB) $\downarrow$	CD $\downarrow$	ITD-E ( $\mu$ s) $\downarrow$	ILD-E (dB) $\downarrow$
HRIR-Former (full)	-7.35	0.210	16.4	1.10
w/o sinusoidal encoding	-4.99	0.298	24.2	1.66
w/o ITD/ILD-prediction heads	-7.52	0.207	19.4	1.11
w/o Conv1D refinement	-6.04	0.257	20.8	1.28
w/o $\mathcal{L}_{\text{HRTF}}$	-7.10	0.217	17.3	1.14
w/ MP pre-processing	-6.80	0.225	19.1	1.21

Table 3: Ablation study of HRIR-Former under

M=5

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Head-related transfer function (HRTF) spatial upsampling from sparse measurements is a fundamental challenge in personalized binaural audio. We formulate HRTF upsampling as an operator learning problem and introduce SPARO, a neural operator that maps sparse measurements at a set of spatial directions to the HRTF field, a continuous representation that can be queried at arbitrary positions. SPARO projects the measurements onto a learned set of spherical latent modes, processes the latent modes with Transformer blocks, and decodes the resulting representations at query directions. On SONICOM, using the LAP24 measurement configuration, SPARO attains the best log-spectral distortion (LSD) and interaural level difference (ILD) error at every sparsity level from 3 to 100 measurements (18% lower LSD and 43% lower ILD error than the strongest baseline at 100 measurements) while remaining competitive in interaural time difference (ITD) error. It reconstructs a dense HRTF 15 to 373 times faster than the leading neural-field method RANF. We further validate the approach on HUTUBS, demonstrating its effectiveness across HRTF datasets.

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