IRM2

Antoine Liutkus, Fabian-Robert Stöter Inria and LIRMM, University of Montpellier, France antoine.liutkus@inria.fr

Additional Info

• is_blind: no
• additional_training_data: no

Supplementary Material

• Code: https://github.com/sigsep/sigsep-mus-oracle
• Demos: Not available

Method

Introduction

The Ideal Ratio Mask for power spectrograms (IRM2) is also known as the generalized Wiener filter.

Notations

We write $x$ for the 3-dimensional complex array obtained by stacking the Short-Time Frequency Transforms (STFT) of left and right channels of the mixture. Its dimensions are $F\times T\times 2$, where $F,T$ stand for the number of frequency bands and time frames, respectively. Its values at Time-Frequency (TF) bin $(f,t)$ are written $x(f,t)\in\mathbb{C}^2$, with entries $x_i(f,t)$ for $i\in\{0,1\}$. The mixture is taken as the sum of the sources images: $x(f,t)=\sum_j y_j(f,t)$, which correspond to the isolated instruments and are also stereo.

Underlying theory: locally stationary Gaussian processes

The IRM2 method lies on solid theoretical grounds. It consists in assuming that all channels are independent and locally stationary Gaussian processes. A description of this model may be found in:

Liutkus, Antoine, Roland Badeau, and Gäel Richard. "Gaussian processes for underdetermined source separation." IEEE Transactions on Signal Processing 59.7 (2011): 3155-3167.

Basically, this boils down to assuming all the entries of $y_j$ as independent and Gaussian. This is written: $y_{ij}(f,t)\sim\mathcal{N}_c\left(0,v_{ij}(f,t)\right)$, where $v_ij$ is the power spectrogram of $y_{ij}$, and can be understood as its energy that varies over time and frequency.

Separation

Under this model, source estimates are computed very simply as: $\hat{y}_{ij}(f,t)=\frac{v_j(f,t)}{\sum_j' v_{ij'}(f,t)} x(f,t),$

which is often called Ideal Ratio Mask, hence the name of this submission.

Parameter estimation

This submission is an oracle, meaning that it knows the true sources to compute the optimal parameters $v_{ïj}$

Given the true sources $y_j$, the parameters are very simply estimated as the power spectrograms:

$v_{ij}(f,t)=\left|y_{ij}(f,t)\right|^2$

References

• A. Liutkus and F.-R. Stöter, The 2018 Signal Separation Evaluation Campaign, Proceedings of LVA/ICA, 2018

@inproceedings{sisec2018, title={The 2018 signal separation evaluation campaign}, author={A. Liutkus and F.-R. St{"o}ter and N. Ito}, booktitle={International Conference on Latent Variable Analysis and Signal Separation}, year={2018}, }