DNN-Based Frequency Component Prediction
for Frequency-Domain Audio Source Separation
Rui Watanabe∗ , Daichi Kitamura∗ , Hiroshi Saruwatari† , Yu Takahashi‡ , and Kazunobu Kondo‡∗ National Institute of Technology, Kagawa College, Kagawa 761–8058, Japan† The University of Tokyo, Tokyo 113–8656, Japan

I. I NTRODUCTION
Audio source separation (ASS) is a technique to estimate
specific audio sources from an observed mixture signal andis a critical preprocessing for machine listening (audio understanding by machine), which finds applications in various
fields. In particular, multichannel ASS (MASS) has recently
attracted attention because typical audio devices (e.g., smart
speakers) have a microphone array. One of the popular MASS
algorithms is multichannel nonnegative matrix factorization(multichannel NMF: MNMF) [1], [2]. MNMF estimates both aspatial model (acoustic paths from sources to microphones) asa source-frequency-wise spatial covariance matrix (SCM) [3]and a source model as a low-rank time-frequency structure ofeach source by NMF [4], [5]. Then, the separation filter ineach frequency bin is calculated using the estimated spatialand source models, resulting in frequency-domain MASS.
Although MNMF separates sources well without any priorinformation or training, it requires a huge computational costfor estimating the parameters.
Deep neural networks (DNNs) have also been principallyused for solving various tasks, and DNN-based single-channel
ASS has been widely investigated [6]–[8]. Although DNNbased MASS [9]–[12] has the potential to achieve highquality separation, it is still challenging to implement theminto a consumer product because of their large-scale networkarchitectures.

Source 1
Frequencydomain MASS
Separation filter

Frequency

Microphone 2

Separation filter

Time

Source 2

Separation filter
Separation filter

Time

Time

Source 1(fullband)

Microphone 1
Source 1(low-freq. band)

Time

Microphone 2

Frequencydomain MASSTime

Separation filter
Source 2(low-freq. band)

Source 2 Time(fullband)

Freq.

Separation filter

DNN-basedfrequency
component
prediction

Freq.

Frequency(a) Conventional MASS

Time

Time

Time

(b) Proposed MASS framework

Fig. 1. Frameworks of (a) conventional and (b) proposed MASS. In proposed
framework, frequency-domain MASS is applied to only limited number of
frequency bins and other frequency components are predicted by DNN.

In this paper, we propose a new, simple, and efficient
MASS framework employing both conventional frequencydomain MASS and DNN-based frequency component prediction. The framework consists of two steps: (a) applying
frequency-domain MASS to narrowband (limited number of)
frequency bins and (b) predicting the source components
in other frequency bins using a small-scale simple DNN
to construct fullband estimated sources. These processes areillustrated in Fig. 1. Since the number of frequency bins canbe reduced in the MASS step, the total computational costis reduced if the DNN prediction step is efficient, which canbe achieved by using edge-computing devices. In this paper,
we only treat MNMF [2] as an example of popular MASS,
but any frequency-domain ASS algorithm (e.g., [13]–[15]) is
applicable in the proposed framework.
II. F REQUENCY- DOMAIN MASS
A. Formulation
Let N and M be the numbers of sources and microphones.
The observed multichannel source and mixture signals obtained by the short-time Fourier transform (STFT) are defined
as follows:This work was partly supported by NVIDIA GPU Grant and JSPS KAKENHI Grant Numbers 19K20306 and 19H01116.

978-9-0827-9705-3

Microphone 1

Time

Frequency

Abstract—Multichannel audio source separation (MASS) plays
an important role in various audio applications. Frequencydomain MASS algorithms such as multichannel nonnegative
matrix factorization achieve better separation quality. However,they require a considerable computational cost for estimating
the frequency-wise separation filter. To solve this problem, we
propose a new framework combining the MASS algorithms anda simple deep neural network (DNN). In the proposed framework, frequency-domain MASS is performed only in narrowband frequency bins. Then, DNN predicts the separated sourcecomponents in other frequency bins, where both the observed
mixture of all frequency bins and the separated narrowband
source components are used as DNN inputs. Our experimental
results show the validity of the proposed MASS framework interms of computational efficiency.
Index Terms—audio source separation, deep neural networks,
frequency component prediction

Frequency‡ Yamaha Corporation, Shizuoka 430–8650, Japan805

sijn = (sijn1 , · · · , sijnm , · · · , sijnM )T ∈ CN ,T

M

xij = (xij1 , · · · , xijm , · · · , xijN ) ∈ C ,

(1)
(2)

EUSIPCO 2020

where i = 1, 2, . . . , I, j = 1, 2, . . . , J, n = 1, 2, . . . , N , andm = 1, 2, . . . , M are the indices of frequency bins, timeframes, sources, and microphones, respectively. We also define
the notations of the spectrogram matrix for (1) and (2) as
Snm ∈ CI×J and Xm ∈ CI×J , respectively. The multichannel
source signal sijn is often called source image. The observed
multichannel mixture
P signal is assumed to be the sum of source
images as xij = n sijn .
B. State-of-the-Art MASS: MNMF
In MNMF [2], the following generative model is assumed
for the source image:sijn ∼ N (0, σijn Hin ),X
σijn =
zkn tik vkj ,

(3)
(4)

k

where N (0, σijn Hin ) is a zero-mean multivariate Gaussian
distribution with the covariance matrix σijn Hin . Also, tik ≥ 0
and vkj ≥ 0 are the NMF parameters (basis and activation),k = 1, 2, . . . , K is the index of NMF bases, and zkn ∈ R[0,1] isa partitioning parameter that clusters K bases into N sources.
The parameter σijn is called source model that corresponds tothe expectation of the power spectrogram of each source. The
time-invariant matrix Hin ∈ CM×M is called spatial modelor SCM that encodes acoustic paths from the source to all
microphones and their spatial spreads.
The parameters σijn and Hin are optimized on the basisof maximum likelihood estimation. In particular, the update
calculation of SCM Hin requires a huge computational costbecause it includes matrix inversions of size M matrices ineach time-frequency slot as follows:

1/2
−1/2
−1/2
1/2
1/2
Rin ,
(5)
Hin ← Rin
Rin Ain Rin
X
−1
Rin =
zkn tik vkj Dij
,
(6)
j,k

Dij =

X

σijn Hin ,(7)

Fig. 2. Input vector for DNN.

To solve this problem, we propose a new framework combining frequency-domain MASS and frequency component
prediction using a small-scale simple DNN. In this framework,
as shown in Fig. 1, MASS is applied to only a limited numberof frequency bins (low-frequency band in Fig. 1). Then, theseparated source components of other frequency bins (highfrequency band in Fig. 1) are predicted using DNN, where
the input data of DNN are both (a) the narrowband separated
source components and (b) the other frequency componentsof the mixture signal. Since we utilize not only (a) but also(b) in the DNN-prediction step, the source components canbe predicted with high accuracy even if we use a small-scale
simple DNN architecture, which may be implementable intoa typical consumer product.
For the sake of simplicity, this paper only treats a two-source
mixture case (N = 2). However, the proposed framework can
be applied to mixtures of more than two sources by simply
extending the DNN model described below. Also, we only
consider to divide spectrograms into low- and high-frequency
bands, and MASS is applied to only the low-frequency band as
shown in Fig. 1. Note that any frequency bins can be selected
as the input in the frequency-limited MASS step.

n
Ain = Hin 

B. DNN Input


X

−1
−1 
zkn tik vkj Dij
xij xHHin .
ij Dij(8)j,kThe separated source image ŝijn is obtained using a multichannel Wiener filter with the estimated parameters σijn and
Hin as−1ŝijn = (σijn Hin ) Dij
xij .

(9)

III. P ROPOSED F RAMEWORK
A. Motivation and Strategy
Although existing frequency-domain MASS methods, including MNMF, can accurately separate the sources, it remains
difficult to implement them for a consumer product becauseof their algorithmic complexity. A large-scale DNN is also notsuitable for edge computing on a memory-limited small device
such as a smart speaker.

I×J
Let Y1 ∈ RI×J
≥0 and Y2 ∈ R≥0 be the amplitude spectrograms of two source signals, and let M ∈ RI×J
≥0 be theamplitude spectrogram of their mixture signal. Since we havethe multichannel source and observation signals, the monaural
amplitude spectrograms Y1 , Y2 , and M are defined using areference microphone, e.g., Y1 = abs(S11 ), Y2 = abs(S21 ),and M = abs(X1 ), where abs(·) returns a matrix with theelement-wise absolute value of the input matrix. In addition,
let i = I 0 be a boundary frequency bin. As shown in Fig. 2, thespectrogram Yn is divided into the low- andhigh-frequency(L)(H)(I−I 0 )×J
I 0×J
bands as Yn ∈ R≥0
and Yn ∈ R≥0, respectively.
Similarly, the narrowband spectrogramsofM
aredefined as(I−I 0 )×J
I 0×J
M (L) ∈ R≥0
and M (H) ∈ R≥0.
The DNN model predicts the high-frequency narrowband
source components, which are not separated in the MASS step,(L)from the low-frequency narrowband separated sources, Y1

806

(I−I 0 )×J

Let Wn ∈ R[0,1]be the soft mask that enhances thehigh-frequency narrowband nth source components asYn(H) ≈ Wn

Fig. 3. DNN architecture.
(L)and Y2 , and the high-frequency narrowband mixture M (H) .
More precisely, the DNN outputs two soft masks that enhance(H)(H)
Y1 and Y2 from M (H) .
The input vector of the DNN model is shown in Fig. 2. The
high-frequency mixture and the low-frequency source vectors
at a time frame j are defined as

T
(H)
(H)
(H)
(H)
I−I 0
mj = m1j , m2j , · · · , m(I−I 0 )j
∈ R≥0
,
(10)
T

0
(L)
(L)
(L)
(L)
∈ RI≥0 ,(11)
ynj = yn1j , yn2j , · · · , ynI 0 j
(H)

(L)

where mij and ynij are the ij elements of M (H) and(L)
Yn , respectively. When the DNN predicts the high-frequency
source components at time frame j, the components around j
are also important. Thus, we concatenate the neighboring timeframes1 of (10) and (11) to define the input vector for DNN
as follows:

T
(H)
(H) T
(H) T
(H) T
mj = mj−2c , · · · , mj
, · · · , mj+2c
,
(12)
(L)



(L)

T

(L) T

(L)

T

, · · · , yn(j+2c), (13)


(H) T
(L) T
(L) T
(2C+1)(I+I 0 ), y 1j , y 2j
∈ R≥0
,
(14)
bj = mjy nj =yn(j−2c) , · · · , ynj

Twhere c = 0, 1, . . . , C is the index of neighboring time frames.
The vector bj is normalized to make the DNN training stable,
where the normalization coefficient is provided so that thevolume can still be exploited asT1(2C+1)(I+I 0 )+1
dj =
bT
,
kb
k
,
(15)
∈ R≥0
j 2
j
kbj k2where k · k2 denotes the L2 norm. The input vector for the
proposed DNN model is (15).
C. DNN Output and Model Training
Fig. 3 shows the architecture of DNN. The network is fully
connected and has four hidden layers, where all the hidden
layers have the same number of units (dimensions) as in the
output layer. Swish [16] is used as an activation function of
all the hidden layers. For the output layer, the frequency-wise
softmax function is applied because the sum of the soft masksof all the sources must be one in each frequency bin.
1 The reason we skip a time frame as j − 2, j, j + 2 is that adjacent timeframes include redundant information by half shifting in the STFT.

M (H) ,

(16)

where denotes the element-wise product. The output vectorof DNN, w̃j , is a concatenation of column vectors of the soft
mask matrices W1 and W2 at the time frame j as follows:2(I−I 0 )T
T Tw̃j = w1j
, w2j
∈ R[0,1] ,
(17)
T
0
(18)
wnj = wn1j , wn2j , · · · , wn(I−I 0 )j ∈ RI−I
[0,1] ,
P
where wnij is the element of Wn and n wnij = 1 is ensured
for all i and j by the softmax function of the output layer.
The label (ground truth) vector of the high-frequency sourcecomponents is obtained asT2(I−I 0 )
(H) T
(H) T
∈ R≥0
ỹj = y1j , y2j
,
(19)
T

0
(H)
(H) (H)(H)
ynj = yn1j , yn2j , · · · , yn(I−I 0 )j
∈ RI−I
≥0 ,
(H)

(20)

(H)

where ynij is the element of Yn . Thus, the DNN modelis trained so that the following mean squared error (MSE) is
minimized:1kỹj − w̃j m̃j k22 , (21)MSE(ỹj , w̃j m̃j ) =2(I − I 0 )


(H) T
2(I−I 0 )
(H) T
, mj
∈ R≥0
. (22)
m̃j = mj
D. Reconstruction of Separated Time-Domain Signals
In the test stage, the low-frequency narrowband separated(L)(L)
sources, Y1 and Y2 , and the high-frequency narrowband
mixture M (H) are input to the pretrained DNN model, andthe framewise soft mask w̃j is predicted. The estimatedhigh-frequency components are obtained by (16). Thus, theestimated amplitude spectrogram Yn can be obtained by(H)(L)
concatenating Yn and Yn .
To reconstruct the time-domain signal of Yn , phase infor(H)mation of Yn must be recovered. In the proposed method,
we simply copy the phase spectrogram of the mixture M (H)(H)(H)
to both Y1
and Y2 , and the inverse STFT is applied toeach complex-valued spectrogram.
IV. E XPERIMENTS
To confirm the validity of the proposed framework, we
conducted two experiments: (a) comparison of net prediction
ability of frequency components based on DNNs and (b)MASS experiment using a music mixture of drums (Dr.) andvocals (Vo.).
A. Comparison of Net Prediction Ability
1) Conditions: In this experiment, the validity of the proposed DNN model was confirmed by comparing net prediction
ability of frequency components based on DNNs, namely, weevaluated how much the prediction was improved by adding
the narrowband mixture M (H) to the DNN input. We trained
two DNN models: DNN w/o mixture and DNN w/ mixture.

807

DNN w/o mixture can be interpreted as a simple bandwidth
expansion based on DNN [17], [18] because this model pre(I−I 0 )×J
dicts the high-frequency narrowband source P (H) ∈ R≥0
I 0×J
from only the low-frequency narrowband source P (L) ∈ R≥0,
where P (H) and P (L) are the amplitude spectrograms ofa source signal. The input and label vectors of DNN w/omixture, qj and p(H) , are respectively defined asT1(2C+1)I 0 +1
qj =
pT
,
kp
k
∈ R≥0
,
(23)
j 2
j
kpj k2

T
T
T
(L)
(L)
(L) T
(L)
,
(24)
pj = p(j−2c) , · · · , pj , · · · , p(j+2c)T0(L) (L)(L)= p1j , p2j , · · · , pI 0 j∈ RI≥0 ,T
0(H)(H) (H)(H)
pj = p1j , p2j , · · · , p(I−I 0 )j
∈ RI−I
≥0 ,
(L)

pj

(L)

(H)

TABLE IS ONG NAMES OF DRY SOURCE IN TEST DATASETSong ID
12
3
4Song namedev1 bearlin-roads
dev2 another dreamer-the ones we lovedev2 fort minor-remember the namedev2 ultimate nz tour

TABLE IISAR S OF PREDICTED FULLBAND SOURCE SIGNALSong ID

DNN w/o mixtureDr.: 21.1 dB
Vo.: 21.8 dB

DNN w/ mixtureDr.: 28.0 dB
Vo.: 31.5 dB

2

Dr.: 22.0 dB
Vo.: 12.7 dB

Dr.: 21.8 dB
Vo.: 19.6 dB

3

Dr.: 15.0 dB
Vo.: 11.2 dB

Dr.: 20.4 dB
Vo.: 18.5 dB

4Dr.: 11.0 dB
Vo.: 10.4 dB

Dr.: 18.2 dB
Vo.: 15.3 dB

1

(25)
(26)

where pij and pij are the elements of P (L) and P (H) ,respectively. Phase information of P (H) was recovered byapplying the GriffinLim algorithm [19]. Since DNN w/omixture does not require multiple sources as the input, thetraining was carried out using one source, resulting in a sourcedependent bandwidth expansion model. Thus, two DNNs w/o
mixture for Dr. and Vo. were prepared. DNN w/ mixture is the
proposed DNN model explained in Sect. III, which requires(L)(L)
Y1 , Y2 , and M (H) as the input and predicts the soft masks
(H)
(H)
(L)
for obtaining Y1
and Y2 . In this experiment, Y1 and(L)
Y2 in DNN w/ mixture were set to completely separated
source components. This condition simulates the situation that
the MASS step in the proposed framework ideally separates
the sources in each frequency bin.
The DNN models were trained with Dr. and Vo. of 100
songs obtained from the SiSEC2016 [20] MUS dataset. The
hamming window length and its shift length in STFT were set
to 128 ms and 64 ms, respectively, where I = 1025 (8 kHz).
(H)
The input and label vectors (qj and pj for DNN w/o mixtureand dj and ỹj for DNN w/ mixture) were produced as thetraining pairs, where the mixture M is the sum of the two
dry sources in the time domain. The boundary frequency bin
was set to I 0 = 512 (4 kHz), and the four neighboring timeframes were input (C = 2). We used Adam [21] to optimize
the DNN model, and its hyperparameters were ε = 1.0×10−8 ,β1 = 0.9, β2 = 0.999, and η = 0.001. The minibatch size was128, and the number of epochs was 1000.
As the test sources of Dr. and Vo., we used four songs shownin Table I from the SiSEC2011 [23] dataset. We evaluatedsources-to-artifacts ratio (SAR) [24] of the reconstructed fullband source signals, where SAR shows the absence of artificial
distortion.
2) Results: Table II shows SARs of the fullband source
signals predicted by each DNN model. Although DNN w/omixture is a source-dependent bandwidth expansion model,
the proposed DNN model outperforms DNN w/o mixture
owing to the utilization of the high-frequency narrowband
mixture. This fact shows the validity of the proposed DNN

Signal length [s]
14.0
25.0
24.0
18.0

model. The efficiency of the proposed MASS framework
combining MNMF and DNN w/ mixture is evaluated in thenext subsection.
B. MASS Experiment Using Music Mixture1) Conditions: In this experiment, we produced a mixtureof Dr. and Vo. observed by two microphones (N = M = 2),
where RWCP [22] E2A impulse responses shown in Fig. 4
were convoluted to each dry source. As the dry sourcesof Dr. and Vo., we used the same sources as shown in
Table I. In the MASS step, we used MNMF with 13 NMF
bases (K = 13), which gave better separation results in thisexperiment. The initial SCMs were set to identity matrices, andall the other parameters were initialized with random values.
As the measure of source separation performance, we usedsource-to-distortion ratio (SDR) [24], which shows both thedegree of separation and the quality of the separated source.
The calculations in MNMF were carried out on an AMD
Ryzen 7 2700X CPU. The DNN prediction was calculated
on an NVIDIA GeForce RTX2080Ti GPU.
2) Results: Fig. 5 shows the averaged SDRs of MNMF witha fullband mixture (fullband MNMF) and MNMF with a narrowband mixture followed by the DNN prediction (proposed
method). The horizontal axis indicates the average elapsed
time of each method, where the results of the proposed method
include the calculation time for the DNN prediction, which isless than 0.1 s. Since the elapsed time depends on the numberof iterations of the MNMF parameter update (denoted as L),
we performed the proposed method using various numbers of
iterations in MNMF, that is, L = 10, 20, . . . . Thus, each plotof the proposed method in Fig. 5 shows the result for each of
the L conditions. Fullband MNMF was also performed morethan L = 300 iterations, and the SDR behaviors are also shownin Fig. 5. In addition, MNMF was performed 10 times withdifferent pseudorandom seeds in both fullband MNMF and the
proposed method, and the average SDRs are shown in Fig. 5.
From these results, we can confirm that the proposed
method can reduce the computational cost by almost half
compared with fullband MNMF. For example, in Fig. 5 (d),

808

Dr.

E2A impulse 20
response
T60 = 300 ms

2m

R EFERENCES

Vo.

40 Mic. spacing
5.66 ms

Fig. 4. Impulse responses used in experiment.

Fig. 5. Average SDRs and their average elapse times: (a) song ID=1, (b)song ID=2, (c) song ID=3, and (d) song ID=4. Each plot of proposed method
shows result for each of L conditions (numbers of iterations in narrowband
MNMF).

the proposed method achieves 13 dB in less than 50 s, whereas
fullband MNMF converged to 13 dB in 120 s. This is because
the number of frequency bins in MNMF is reduced fromI = 1025 to I − I 0 = 512. Also, at the converged point, theproposed method outperforms fullband MNMF in Fig. 5 (a),(b) and (d). This performance of the proposed method was
obtained owing to the accurate estimation of the soft masks
based on the training with 100 songs.
V. C ONCLUSION
In this paper, we presented a new computationally efficient source separation framework combining an existing
ASS technique and a simple-DNN-based frequency component
prediction framework. The proposed framework can reducethe computational cost by decimating frequency bins for audio
source separation and predicting the source components in thedecimated frequency bins. From the experimental results, thevalidity of the proposed framework was confirmed by achieving faster ASS than by using the conventional fullband ASS
algorithm. The proposed framework can easily be extended
to various situations, e.g., ASS is applied once in every few
frequency bins or is applied to only the valid frequency binsthat are effective for source separation.

[1] A. Ozerov and C. Févotte, “Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation,” IEEE Trans.
ASLP, vol. 18, no. 3, pp. 550–563, 2010.
[2] H. Sawada, H. Kameoka, S. Araki, and N. Ueda, “Multichannel extensions of non-negative matrix factorization with complex-valued data,”
IEEE Trans. ASLP, vol. 21, no. 5, pp. 971–982, 2013.
[3] N. Q. K. Duong, E. Vincent, and R. Gribonval, “Under-determined
reverberant audio source separation using a full-rank spatial covariancemodel,” IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, 2010.
[4] D. D. Lee and H. S. Seung, “Learning the parts of objects by nonnegative matrix factorization,” Nature, vol. 401, pp. 788–791, 1999.
[5] C. Févotte, N. Bertin, and J.-L. Durrieu, “Nonnegative matrix factorization with the Itakura-Saito divergence: With application to music
analysis,” Neural Computation, vol. 21, no. 3, pp. 793–830, 2009.
[6] E. M. Grais, M. U. Sen, and H. Erdogan, “Deep neural networks for
single channel source separation,” Proc. ICASSP, pp. 3734–3738, 2014.
[7] P.-S. Huang, M. Kim, M. H.-Johnson, and P. Smaragdis, “Joint optimization of masks and deep recurrent neural networks for monaural source
separation,” IEEE/ACM Trans. ASLP, vol. 23, no. 12, pp. 2136–2147,
2015.
[8] J. R. Hershey, Z. Chen, J. Le Roux, and S. Watanabe, “Deep clustering: discriminative embeddings for segmentation and separation,” Proc.
ICASSP, pp. 31–35, 2016.
[9] S. Araki, T. Hayashi, M. Delcroix, M. Fujimoto, K. Takeda,
and T. Nakatani, “Exploring multi-channel features for denoisingautoencoder-based speech enhancement,” Proc. ICASSP, pp. 116–120,
2015.
[10] A. A. Nugraha, A. Liutkus, and E. Vincent, “Multichannel audio source
separation with deep neural networks,” IEEE/ACM Trans. ASLP, vol. 24,
no. 9, pp. 1652–1664, 2016.
[11] T. Nakatani, N. Ito, T. Higuchi, S. Araki, and K. Kinoshita, “Integrating
DNN-based and spatial clustering-based mask estimation for robust
MVDR beamforming,” Proc. ICASSP, pp. 286–290, 2017.
[12] N. Makishima, S. Mogami, N. Takamune, D. Kitamura, H. Sumino,
S. Takamichi, H. Saruwatari, and N. Ono, “Independent deeply learned
matrix analysis for determined audio source separation,” IEEE/ACM
Trans. ASLP, vol. 27, no. 10, pp. 1601–1615, 2019.
[13] H. Sawada, S. Araki, and S. Makino, “Underdetermined convolutive
blind source separation via frequency bin-wise clustering and permutation alignment,” IEEE Trans. ASLP, vol. 19, no. 3, pp. 516–527, 2010.
[14] D. Kitamura, N. Ono, H. Sawada, H. Kameoka, and H. Saruwatari, “Determined blind source separation unifying independent vector analysis
and nonnegative matrix factorization,” IEEE/ACM Trans. ASLP, vol. 24,
no. 9, pp. 1626–1641, 2016.
[15] K. Yatabe and D. Kitamura, “Time-frequency-masking-based determined
BSS with application to sparse IVA,” Proc. ICASSP, pp. 715–719, 2019.
[16] P. Ramachandran, B. Zoph, and Q. V. Le, “Searching for activation
functions,” arXiv preprint, arXiv:1710.05941, 2017.
[17] K. Li and C.-H. Lee, “A deep neural network approach to speech
bandwidth expansion,” Proc. ICASSP, pp. 4395–4399, 2015.
[18] Y. Wang, S. Zhao, W. Liu, M. Li, and J. Kuang, “Speech bandwidth
expansion based on deep neural networks,” Proc. INTERSPEECH,
pp. 2593–2597, 2015.
[19] D. Griffin and J. Lim, “Signal estimation from modified shorttime
Fourier transform,” IEEE Trans. ASSP, vol. 32, no. 2, pp. 236–243,
1984.
[20] A. Liutkus, F.-R. Stöter, Z. Rafii, D. Kitamura, B. Rivet, N. Ito, N. Ono,and J. Fontecave, “The 2016 signal separation evaluation campaign,”
Proc. LVA/ICA, pp. 323–332, 2012.
[21] D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,”
arXiv preprint, arXiv:1412.6980, 2014.
[22] S. Nakamura, K. Hiyane, F. Asano, T. Nishiura, and T. Yamada, “Acoustical sound database in real environments for sound scene understanding
and hands-free speech recognition,” Proc. LREC, pp. 965–968, 2000.
[23] S. Araki, F. Nesta, E. Vincent, Z. Koldovský, G. Nolte, A. Zieheand A. Benichoux, “The 2011 signal separation evaluation campaign(SiSEC2011):-audio source separation,” Proc. Latent Variable Analysis
and Signal Separation, pp. 414–422, 2012.
[24] E. Vincent, R. Gribonval, and C. Fevotte, “Performance measurementin blind audio source separation,” IEEE Trans. ASLP, vol. 14, no. 4,
pp. 1462–1469, 2006.

809