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- 1. Regularized Superresolution-Based Binaural Signal Separation with 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)
- 2. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 2
- 3. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 3
- 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. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 5
- 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. 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 sound Supervision sound
- 8. Penalized Supervised NMF (PSNMF) • In PSNMF, the following decomposition is addressed under the condition that is known in advance. [Yagi, et al., 2012] 8 Separation process Fix trained bases and update . is forced to become uncorrelated with Update Training process Supervised bases of the target sound Supervision sound Problem of PSNMF: When the signal includes many sources, the extraction performance markedly degrades.
- 9. Directional Clustering • Directional clustering can estimate sources and their direction in multichannel signal. [Araki, et al., 2007] [Miyabe, et al., 2009] • This method can separate sources with spatial information in an observed signal. 9 L R L-chinputsignal R-ch input signal ：Source component ：Centroid vector
- 10. Directional Clustering • Directional clustering can estimate sources and their direction in multichannel signal. [Araki, et al., 2007] [Miyabe, et al., 2009] • This method can separate sources with spatial information in an observed signal. 10 L R L-chinputsignal R-ch input signal ：Source component ：Centroid vector Problem of directional clustering: This method cannot separate sources in the same direction.
- 11. Hybrid method • Conventional hybrid method utilizes PSNMF after the directional clustering. [Iwao, et al., 2012] • This method consists of two techniques. – Directional clustering – PSNMF 11 Directional clustering L R PSNMF Spatial separation Source separation Conventional Hybrid method
- 12. Problem of hybrid method • The signal extracted by the hybrid method suffers from the generation of considerable distortion due to the binary masking in directional clustering. • The signal in the target direction, which is obtained by directional clustering, has many spectral chasms. • The resolution of the spectrogram is degraded. 12 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 TimeFrequency : Other direction ：Hadamard product (product of each element) Input spectrogram Binary mask Separated cluster Directional Clustering
- 13. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 13
- 14. Proposed hybrid method 14 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.
- 15. Regularized superresolution-based NMF • In proposed supervised NMF, the spectral chasms are treated as unseen observations using index matrix. 15 : 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
- 16. Regularized superresolution-based NMF • The spectrogram of the target sound is reconstructed using more matched bases because chasms are treated as unseen. • The components of the target sound lost after directional clustering can be extrapolated using supervised bases. 16 Time Frequency Separated cluster Time Frequency Reconstructed spectrogram : Chasms Supervised bases Superresolution using supervised bases
- 17. 17 Regularized superresolution-based NMF • Signal flow of the proposed hybrid method Center RightLeft Direction sourcecomponent (a) Frequencyof Observed spectra Target source
- 18. 18 Target direction Regularized superresolution-based 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
- 19. 19 Regularized superresolution-based 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
- 20. 20 Regularized superresolution-based 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
- 21. Regularized superresolution-based 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. 21 4 3 2 1 0 Frequency[kHz] 43210 Time [s] Extrapolation error (incorrectly modifying the activation) Time Frequency Separated cluster Almost unseen frame
- 22. Regularized superresolution-based NMF • We propose two types of regularizations. 22 Regularization of the temporal continuity Regularization of the 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 Previous frame The intensity of these regularizations are proportional to the number of chasms in each frame.
- 23. Regularized superresolution-based NMF • The cost function in regularized superresolution-based NMF is defined using the index matrix as 23 : Regularization term : Penalty term to force and to become uncorrelated with each other : Weighting parameter
- 24. Regularized superresolution-based NMF • The update rules that minimize the cost function are obtained as follows: 24
- 25. Outline • 1. Research background • 2. Conventional method – Nonnegative matrix factorization – Penalized supervised nonnegative matrix factorization – Directional clustering – Hybrid method • 3. Proposed method – Regularized superresolution-based nonnegative matrix factorization • 4. Experiments • 5. Conclusions 25
- 26. Evaluation experiment • We compared four methods. – Conventional hybrid method using PSNMF (Conventional method) – Proposed hybrid method using superresolution-based NMF without regularization (Proposed method 1) – Proposed hybrid method using superresolution-based NMF with regularization of the temporal continuity (Proposed method 2) – Proposed hybrid method using superresolution-based NMF with regularization of the norm minimization (Proposed method 3) 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. Evaluation experiment • We used stereo-panning signals ( ) and binaural- recorded signals ( ) containing four instruments, Ob., Fl., Tb., and Pf., generated by MIDI synthesizer. • The sources are mixed as the same power. • Target source is always located in the center direction (no.1). • 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. Experimental results (panning signal) • Average SDR, SIR, and SAR scores for each method, where the 4 instruments are shuffled with 12 combinations. 28 12 10 8 6 4 2 0 SDR[dB] 24 20 16 12 8 4 0 SIR[dB] 10 8 6 4 2 0 SAR[dB] SDR ：quality of the separated target sound SIR ：degree of separation between the target and other sounds SAR ：absence of artificial distortion Proposed method 1 ：no regularization Proposed method 2 ：regularization of temporal continuity Proposed method 3 ：regularization of norm minimization SDR SIR SARGood Bad
- 29. Experimental results (binaural signal) • Average SDR, SIR, and SAR scores for each method, where the 4 instruments are shuffled with 12 combinations. 29 6 5 4 3 2 1 0 SAR[dB] 20 16 12 8 4 0 SIR[dB] 10 8 6 4 2 0 SDR[dB] SDR ：quality of the separated target sound SIR ：degree of separation between the target and other sounds SAR ：absence of artificial distortion SDR SIR SAR Proposed method 1 ：no regularization Proposed method 2 ：regularization of temporal continuity Proposed method 3 ：regularization of norm minimization Bad Good
- 30. Conclusions • We propose a new supervised NMF algorithm, which is superresolution-based method, for the hybrid method to separate stereo or binaural signals. • The proposed hybrid method can separate the target signal with high performance compared with conventional method. • The regularization of norm minimization is effective for the proposed supervised NMF algorithm. 30 Thank you for your attention!