aspcore.lowrank

Implements algorithms related to low-rank tensor approximations of impulse responses

• Decomposes and reconstructs any impulse response with singular value decomposition or canonical polyadic decomposition for a low-rank approximation [jalmbyLowrank2021, paleologuLinear2018]

• Implements a low-cost convolution by directly using the low-rank representation [atkinsApproximate2013, jalmbyFast2023]

References

[jalmbyLowrank2021] M. Jälmby, F. Elvander, and T. van Waterschoot, “Low-rank tensor modeling of room impulse responses,” in 2021 29th European Signal Processing Conference (EUSIPCO), Aug. 2021, pp. 111–115. doi: 10.23919/EUSIPCO54536.2021.9616075. [link]

[paleologuLinear2018] C. Paleologu, J. Benesty, and S. Ciochină, “Linear system identification based on a Kronecker product decomposition,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 26, no. 10, pp. 1793–1808, Oct. 2018, doi: 10.1109/TASLP.2018.2842146. [link]

[atkinsApproximate2013] J. Atkins, A. Strauss, and C. Zhang, “Approximate convolution using partitioned truncated singular value decomposition filtering,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, May 2013, pp. 176–180. doi: 10.1109/ICASSP.2013.6637632. [link]

[jalmbyFast2023] M. Jälmby, F. Elvander, and T. van Waterschoot, “Fast low-latency convolution by low-rank tensor approximation,” in ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes, Greece, Jun. 2023. [link]

Functions

create_filter([ir, num_in, num_out, rank, ...])	Returns the appropriate low rank filter.
decompose_ir(ir, dims, rank)	Decomposes an IR into a Kronecker / Tensor product decomposition of rank rank.
reconstruct_ir(ir_decomp[, out])	Takes a decomposition of an IR and reconstructs the IR.