3-5-11

スペシャル・セッション〔国際セッション〕

Improving the robustness of multiple input spectrogram inversion ∗○ Dongxiao Wang†
Hirokazu Kameoka‡
Koichi Shinoda††Tokyo Institute of Technology‡
NTT Communication Science Laboratories

1Introduction

In MISI, the summation of each source should ex-

We focus on the single channel source separation(SCSS) problem where multiple sources are collectedby a single sensor. While most of its studies have neglected the phase information, it becomes essential
for some applications such as hearing aid devices.
To estimate phases, Gunawan et al.[1] proposedmultiple input spectrogram inversion (MISI). Whileit significantly improves the quality of recovered signals when the true magnitude spectrogram of each

actly be the mixture signal. This constraint is often
too hard to be satisfied. Another observation is thatthe error between mixture signal ỹ and the sum of∑estimated signal j ′ W+ (aj ′ ⊙ ϕj ′ ) is equally distributed over all sources. This also may not be practical since this error can be diﬀerent from source tosource.

3

Modified MISI

underlying source is given, the performance drops

To mitigate the two problems mentioned above,

drastically when only erroneous magnitude spectro-

we propose a new algorithm, Modified MISI (M-grams or only some of them are available.
In this paper, we propose an algorithm that is ro-MISI), which employs a diﬀerent objective function:
minimizebust against the uncertainty of the magnitude spec-I(ϕ) =∑2

aj ⊙ ϕj − WW+ (aj ⊙ ϕj ) 2jtrum. In addition, it is flexible enough to allow for+λ y−

the presence of residual components. It also deals∑(5)2aj ⊙ ϕj.

j

2

with the diﬀerent degrees of uncertainty among theHere y is a vector of the complex spectrogram ofcomponent signals.

the mixture signal. The first term of (5) measures

2how much the estimated phase spectrogram satisfies

Previous Studies

the constraint introduced by overlapping windowHere we briefly introduce Multiple Input Spectro-

ing function in STFT. The second term measuresgram Inversion (MISI). When given the mixture sig-

the distance between the mixture spectrogram andnal ỹ and magnitude spectrogram aj of each sourcej, this algorithm estimates signal c̃j and phase ϕj

the sum of estimated spectrogram of each source,
relaxes the hard constraint (2) in the original MISI.

by solving the following optimization problem:

Note that it is not always necessary to satisfy (2).

minimizesubject toJ (ϕ, c̃) =∑∑2aj ⊙ ϕj − Wc̃j 2 ,(1)jc̃j = ỹ.

(2)

jIn addition we introduce weight β for each compo∑
nent signal where j βj,f,n = 1, 0 < βj,f,n < 1. Let∑yf,n = j xj,f,n , and the vector notation of xj,f,nbe xj . By solving (5) in the similar way with [2], weHere W denotes short time Fourier transform(STFT). Since it is diﬃcult to solve them directly,

get the update rules of each variable:c̃j ← W+ (aj ⊙ ϕj )it utilizes an iterative process:xj ← aj ⊙ ϕj + β j ⊙ y −

∑(())
1c̃j ← W+ aj ⊙ ϕj + ỹ −W+ aj ′ ⊙ ϕj ′  , (3)J′(ϕj ← ∠jϕj ← ∠Wc̃j ,Here W+ denotes the inverse STFT.

(4)βj ← ∑∑

aj ′ ⊙ ϕj ′ (6)(7)

j′β j ⊙ Wc̃j + λxj)

(8)

β j + λ1abs(xj − aj ⊙ ϕj )j ′ abs(xj ′ − aj ′ ⊙ ϕj ′ ),(9)where 1 is an all-ones vector, ·· denotes the elementwise division and abs(·) denotes an operation that∗

多入力スペクトログラムインバージョンの頑健性の改善、王冬暁、亀岡弘和、篠田浩一

日本音響学会講演論文集- 1307 -2019年3月

Table 1: Comparison of SDR, SAR and SIR among Wiener filtering, MISI and Modified-MISI. Each value
represents the best value in 60 iterations, averaged over 100 experiments.
−10 dB

Noise SSNR
Wiener

0 dB+10 dB+20 dB

SDR

SIR

SAR

SDR

SIR

SAR

SDR

SIR

SAR

SDR

SIR

SAR

12.13

19.55

13.19

12.14

19.41

13.28

12.56

19.98

13.66

12.56

20.09

13.63

MISI

2.87

5.95

8.90

7.84

13.35

11.85

14.34

20.53

17.96

22.79

28.39

26.24

M-MISI

11.95

24.56

12.79

13.27

26.46

14.03

17.45

30.31

18.11

24.45

35.26

25.04

1515

Wiener filtering.

10SSNR=−10 dB

SNR-E

510

SSNR=0 dB

4.2

Experimental Results

Table 1 shows the overall comparison between M-05MISI, MISI, and Wiener filtering. In most cases the-5-10

proposed M-MISI gave significantly better perfor-

00204060

18020406025

mance than MISI and Wiener filtering.
Figure 1 compares SNR-E among those methods.

16SNR-E

20

SSNR=10 dB

14

SSNR=20 dB
1510100204060

02040dB and 0 dB. Our method achieved a larger SNR-Ewith SNR 10 dB and 20 dB.

MISI
Modified MISIWiener

12MISI and M-MISI performed poorly with SNR −1060Fig. 1: Comparison of SNR among Wiener filtering,MISI and Modified-MISI.

5Conclusion
We have proposed a new phase reconstruction al-gorithm, M-MISI, which employs a soft objectivefunction. This algorithm is more robust when mag-takes the absolute value of each element of a vector.

nitude spectra of each source are erroneous. In ourAnd we choose λ as the ratio between the two terms

experiment, the proposed M-MISI showed a signifi-of the objective function.

cant improvement when we added gamma noise on
the simulated data.

4Experimental Evaluation

4.1

Setup

In future, we would like totackle the case when the number of recording channels (microphones) is more than one.

We evaluate the proposed algorithm on synthe-References

sized data assuming that only imperfect magnitude
spectrogram is known beforehand. Here we ran-[1] D. Gunawan and D. Sen,

domly add Gamma noise to the magnitude spec-from single-channel mixtures, IEEE Signal Pro-

trogram of each source with some specific Spectral
Signal-to-Noise( ∑ 2Ratio) (SSNR) defined as: SSNR ≡s10 log10 ∑ f,t nf,t, where s and n stand for signal
2f,tf,t

Iterative phase es-timation for the synthesis of separated sources
cessing Letters, vol. 17, no. 5, pp. 421424, May2010.
[2] J. Le Roux, H. Kameoka, N. Ono, and S.

and noise, respectively. The mixtures are generated

Sagayama,

from the ATR speech database [3]. All utterancesmagnitude stft spectro- gram based on spectro-

are re-sampled to 16 kHz.

gram consistency,

We use Signal-to-Distortion, Interference and Ar-

Fast signal reconstruction fromin Proc. Int. Conf. Digitaltifacts Ratio (SDR, SIR and SAR) as evaluation

Audio Eﬀects, vol. 10, 2010.
[3] A. Kurematsu, K. Takeda, Y. Sagisaka, S.

metrics. We also report SNR in estimation, SNR-Katagiri, H. Kuwabara, and K. Shikano,E defined as the SNR between ground truth signal

japanese speech database as a tool of speechs and the diﬀerence between s and the estimatedrecognition and synthe- sis,signal se . We compare our method with MISI andcation, vol. 9, no. 4, pp. 357363, 1990.

日本音響学会講演論文集- 1308 -AtrSpeech communi-

2019年3月