Resolution upscaling of spatial room impulse response based on elastic net regularisation

Abstract

The spatial resolution of a spatial room impulse
response (SRIR) measured with a spherical microphone array
is fundamentally constrained by the array’s spherical harmonic
order. Starting from order-limited ambisonic signals, the SRIR is
estimated via plane wave decomposition, which involves solving
an underdetermined inverse problem. Notably, both the spatial
sparsity and signal-to-noise ratio (SNR) of the SRIR vary
over time. To account for this, we introduce an elastic net
regularisation framework that combines L1 and L2 penalties.
This approach leverages the known sparsity of early-arriving
waves to promote sparse solutions via L1 regularisation, while
the inclusion of L2 regularisation also ensures the robustness and
interpretability during periods of reduced sparsity. The flexibility
of tuning the regularisation parameter and the L1 ratio allows the
method to adapt to different SRIR structures. An investigation of
applying the elastic net regularisation with different parameters
to upscale the spatial resolution of SRIR is carried out in this
paper. It is shown that elastic net consistently outperforms the
sole L1 (LASSO) or L2 (Tikhonov) regularisation.

Index Terms—Elastic net regularisation, Spatial room impulse
response, Ambisonics, Room Acoustics.

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Identifiers

ORCID for Filippo Maria Fazi: orcid.org/0000-0003-4129-1433

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