Spherical Harmonic Sliced Wasserstein Displacement Interpolation for Acoustic Source and Reflection Density Modeling

Room Impulse Responses estimation is a fundamental problem in spatial audio processing and speech enhancement. In this paper, we build upon our previously introduced diffusion-based inpainting framework for Room Impulse Response interpolation and demonstrate its applicability to enhancing the performance of practical multi-microphone array processing tasks. Furthermore, we validate the robustness of this method in interpolating real-world Room Impulse Responses.

Image-source-method (ISM)-based room impulse response (RIR) simulation is a useful and physically interpretable tool for acoustic scene modeling, but full-order ISM becomes computationally expensive as the reflection order and room complexity increase. We propose a physics-guided framework for fast RIR simulation that preserves the geometric structure of ISM while learning to retain only acoustically important image-source paths during online traversal. To recover energy removed by pruning, the proposed PathRIR uses a lightweight compensation multilayer perceptron to predict the missing late-tail energy envelope and generate a compensation tail whose energy follows that envelope. Experiments on irregular 3D rooms show that PathRIR reduces image-source computation and improves runtime efficiency over a full-order ISM simulator, while achieving low waveform- and decay-related errors. Ablation results show that adding the compensation tail improves waveform fidelity and reduces energy-decay-curve error, reverberation-time error, and direct-to-reverberant-ratio error, with modest runtime overhead.

The image-source model (ISM) is a widely adopted method for efficiently simulating acoustic room impulse responses (RIRs) under specular reflection assumptions. Acoustic paths between source and receiver are traced to lattice points computed from successive reflections over bounding planes of the room. Rectangular rooms bound the total number of image-sources to be polynomial in the RIR's duration or distance $k$ equivalent, with degree equal the number of room dimensions $N$. Direct ISM simulations are therefore compute upper-bound by $O \left ( k^N \right )$, and consider only cases of $N \leq 3$ for tractability and real-world applications. This work proposes an alternative computational method that lowers the asymptotic compute bound to $O \left ( N k^2 \log k \right )$ for integer coordinates and room dimensions via reducing ISM lattice point counting to the classic Gauss circle problem (GCP). We extend the lattice counting model to frequency-dependent and reflection weighted image-sources in higher dimensions, relating solutions between successive dimensions via the convolution operator. Two constructions for realizing RIRs are presented, along with time-frequency controls, error and run-time analysis, and RIR statistics.