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Superresolution-based stereo signal separation via supervised nonnegative matrix factorization

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Presented at IEEE 18th International Conference on Digital Signal Processing (DSP 2013) (international conference)
Daichi Kitamura, Hiroshi Saruwatari, Yusuke Iwao, Kiyohiro Shikano, Kazunobu Kondo, Yu Takahashi, "Superresolution-based stereo signal separation via supervised nonnegative matrix factorization," Proceedings of IEEE 18th International Conference on Digital Signal Processing (DSP 2013), T3C-2, Santorini, Greece, July 2013.

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Superresolution-based stereo signal separation via supervised nonnegative matrix factorization

  1. 1. Superresolution-Based Stereo Signal Separation via Supervised Nonnegative Matrix Factorization Daichi Kitamura, Hiroshi Saruwatari, Yusuke Iwao, Kiyohiro Shikano (Nara Institute of Science and Technology, Nara, Japan) Kazunobu Kondo, Yu Takahashi (Yamaha Corporation Research & Development Center, Shizuoka, Japan) 18th International conference on Digital Signal Processing 2013
  2. 2. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Multichannel NMF – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 2
  3. 3. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Multichannel NMF – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 3
  4. 4. Background • Music signal separation technologies have received much attention. • Music signal separation based on nonnegative matrix factorization (NMF) has been a very active area of the research. • The extraction performance of NMF markedly degrades for the case of many source mixtures. 4 • Automatic music transcription • 3D audio system, etc. Applications We propose a new method for multichannel signal separation with NMF utilizing both spectral and spatial cues included in mixtures of multiple instruments.
  5. 5. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Multichannel NMF – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 5
  6. 6. NMF • NMF is a type of sparse representation algorithm that decomposes a nonnegative matrix into two nonnegative matrices. [D. D. Lee, et al., 2001] 6 Time Frequency AmplitudeFrequency Amplitude Observed matrix (Spectrogram) Basis matrix (Spectral bases) Activation matrix (Time-varying gain) Time Ω: Number of frequency bins 𝑇: Number of frames 𝐾: Number of bases 𝒀: Observed matrix 𝑭: Basis matrix 𝑮: Activation matrix
  7. 7. Penalized Supervised NMF (PSNMF) • In PSNMF, the following decomposition is addressed under the condition that is known in advance. [Yagi, et al., 2012] 7 Separation process Fix trained bases and update . is forced to become uncorrelated with Update Training process Supervised bases of the target soundSupervision sound Problem of PSNMF: When the signal includes many sources, the extraction performance markedly degrades.
  8. 8. Directional Clustering • Directional clustering can estimate sources and their direction in multichannel signal. [Araki, et al., 2007] [Miyabe, et al., 2009] 8 L R L-chinputsignal R-ch input signal :Source component :Centroid vector Center cluster Right clusterLeft cluster Problem of directional clustering: This method cannot separate sources in the same direction.
  9. 9. 9 • Multichannel NMF also has been proposed [Ozerov, et al., 2010] [Sawada, et al., 2012]. • Natural extension of NMF for a multichannel signal • This method uses spectral and spatial cues to achieve the unsupervised separation task. Multichannel NMF Problem of multichannel NMF: This unified method is very difficult optimization problem mathematically. Many variables should be optimized using only one cost function. Multichannel NMF involve strong dependence on initial values and lack robustness.
  10. 10. Hybrid method • Conventional hybrid method utilizes PSNMF after the directional clustering. [Iwao, et al., 2012] • This method consists of two techniques. – Directional clustering – PSNMF 10 Directional clustering L R PSNMF Spatial separation Source separation Conventional Hybrid method
  11. 11. Problem of hybrid method • The signal extracted by the hybrid method has considerable distortion. • There are many spectral chasms in the spectrogram obtained by directional clustering. • The resolution of the spectrogram is degraded. 11 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 Time Frequency : Target direction Time Frequency Time Frequency: Other direction :Hadamard product (product of each element) Input spectrogram Binary mask Separated cluster Directional Clustering : Chasms
  12. 12. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Multichannel NMF – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 12
  13. 13. Proposed hybrid method 13 Input stereo signal L-ch R-ch STFT Directional clustering Center component L-ch R-ch center cluster Index of based SNMF Superresolution- based SNMF Superresolution- ISTFT ISTFT Mixing Extracted signal Input stereo signal L-ch R-ch STFT Directional clustering Center component PSNMFPSNMF L-ch R-ch ISTFT ISTFT Mixing Extracted signal Conventional hybrid method Proposed hybrid method Employ a new supervised NMF algorithm as an alternative to the conventional PSNMF in the hybrid method.
  14. 14. Superresolution-based supervised NMF • In proposed supervised NMF, the spectral chasms are treated as unseen observations using index matrix. 14 : Chasms Time Frequency Separated cluster Chasms Treat chasms as unseen observations. 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 Time Frequency Index matrix 1 : Grid of separated component 0 : Grid of chasm (hole)
  15. 15. Superresolution-based supervised NMF • The components of the target sound lost after directional clustering can be extrapolated using supervised bases. 15 Time Frequency Separated cluster Time Frequency Reconstructed spectrogram : Chasms Supervised bases Superresolution using supervised bases
  16. 16. 16 Superresolution-based supervised NMF • Signal flow of the proposed hybrid method Center RightLeft Direction sourcecomponent (a) Frequencyof Observed spectra Target source
  17. 17. 17 Target direction Superresolution-based supervised NMF • Signal flow of the proposed hybrid method Center RightLeft Direction sourcecomponent z (b) Frequencyof After directional clustering Target source Center RightLeft Direction sourcecomponent (a) Frequencyof Observed spectra Center sources lose some of their components Directional clustering
  18. 18. 18 Superresolution-based supervised NMF • Signal flow of the proposed hybrid method Center RightLeft Direction sourcecomponent z (b) Frequencyof After directional clustering Center sources lose some of their components
  19. 19. 19 Superresolution-based supervised NMF • Signal flow of the proposed hybrid method Center RightLeft Direction sourcecomponent z (b) Frequencyof After directional clustering Center sources lose some of their components Superresolution- based NMF Center RightLeft Direction sourcecomponent (c) Frequencyof After super- resolution- based SNMF Extrapolated target source
  20. 20. Superresolution-based supervised NMF • The basis extrapolation includes an underlying problem. • If the time-frequency spectra are almost unseen in the spectrogram, which means that the indexes are almost zero, a large extrapolation error may occur. • It is necessary to regularize the extrapolation. 20 4 3 2 1 0 Frequency[kHz] 43210 Time [s] Extrapolation error (incorrectly modifying the activation) Time Frequency Separated cluster Almost unseen frame
  21. 21. Superresolution-based supervised NMF • We propose to introduce the regularization term in the cost function. • The intensity of these regularizations are proportional to the number of chasms in each frame. 21 Regularization of norm minimization 𝑰 : Index matrix ∙ : Binary complement 𝑖 𝜔,𝑡: Entry of index matrix 𝑰 𝑔 𝑘,𝑡: Entry of matrix 𝑮 𝑓𝜔,𝑘: Entry of matrix 𝑭
  22. 22. Superresolution-based supervised NMF • The cost function in regularized superresolution-based NMF is defined using the index matrix as follows: • Since the divergence is only defined in grids whose index is one, the chasms in the spectrogram are ignored. 22 : Penalty term to force and to become uncorrelated with each other : Weighting parameter Regularization term Penalty term : an arbitrary divergence function
  23. 23. Superresolution-based supervised NMF • The update rules that minimize the cost function based on KL divergence are obtained as follows: 23
  24. 24. Superresolution-based supervised NMF • The update rules that minimize the cost function based on Euclidian distance are obtained as follows: 24
  25. 25. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Multichannel NMF – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 25
  26. 26. Evaluation experiment • We compared five methods. – Simple directional clustering – Simple PSNMF – Multichannel NMF based on IS-divergence – Conventional hybrid method using PSNMF – Proposed hybrid method using superresolution-based SNMF 26 Input stereo signal L-ch R-ch STFT Directional clustering Center component PSNMFPSNMF L-ch R-ch ISTFT ISTFT Mixing Extracted signal Input stereo signal L-ch R-ch STFT Directional clustering Center component L-ch R-ch center cluster Index of based SNMF Superresolution- based SNMF Superresolution- ISTFT ISTFT Mixing Extracted signal
  27. 27. Evaluation experiment • We used stereo-panning signals ( , ). • Mixture of four instruments (Ob., Fl., Tb., and Pf.) generated by MIDI synthesizer • We used the same type of MIDI sounds of the target instruments as supervision for training process. 27 Center 1 2 3 4 Left Right Target source Supervision sound Two octave notes that cover all notes of the target signal
  28. 28. Experimental results ( ) • Average SDR, SIR, and SAR scores for each method, where the four instruments are shuffled with 12 combinations. 28 SDR :quality of the separated target sound SIR :degree of separation between the target and other sounds SAR :absence of artificial distortion Good Bad SDR SIR SAR
  29. 29. Experimental results ( ) • Average SDR, SIR, and SAR scores for each method, where the four instruments are shuffled with 12 combinations. 29 SDR :quality of the separated target sound SIR :degree of separation between the target and other sounds SAR :absence of artificial distortion Good Bad SDR SIR SAR
  30. 30. Conclusions • We propose a new supervised NMF algorithm for the hybrid method to separate stereo or multichannel signals. • The proposed supervised method recovers the resolution of spectrogram, which is obtained by the binary masking in directional clustering, using supervised basis extrapolation. • The proposed hybrid method can separate the target signal with high performance compared with conventional methods. 30 Thank you for your attention!

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