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>> Ivan Tashev: It's my pleasure to present Ngoc Q.K. Duong here, who is going
to give a talk about probabilistic special modeling capable and how you apply it to
source separation.
He took his Bachelor's degree in his native Vietnam. Took his master's degree in
Korea and is going to finish his Ph.D. in India and France. So this alone is an
interesting part of doing research, most of it in the area of audio signal parsing
[phonetic]. So without further ado, you have the floor.
>> Ngoc Q.K. Duong: Okay. Yes. Thank you for the introduction. And good
morning, everyone. So first I'll briefly again talk a bit about my background. I'm
Ngoc Q.K. Duong. I'm Vietnamese. So for four and a half years I took
Bachelor's degrees in electrical engineering in Post and Telecommunication
Institute in Vietnam.
Then I have almost one and a half years working as a system engineer in
industries, mainly for the Polycom video conferencing products, like audio and
audiovisual. And for two years I moved to the Korea, South Korea, to pursue
master degrees in electrical engineering and mainly on signal processing.
After getting the degrees, I had happy years working as a research engineer in
[inaudible] company, also that companies because on sound and speech
technology which transfer to the more [inaudible] industry.
And then after finishing -- not really finishing with that, I get funding for the Ph.D.
and I move to France, France National Research Institute in [inaudible] India, to
pursue my Ph.D.
Up until now, [inaudible], it will be October of this year. So still four months. So
exactly three years Ph.D.. that is briefly my background.
Today, I'm happy to present my Ph.D. work, probabilistic space model for
rebuilding and diffuse sources applied to audio source separation.
So please feel free to interrupt me at any time for your question or comments.
Okay. Here we go. So problem we're looking at is a cocktail party effects where
we have many sound sources mixed together in meeting room, for instance, or in
a patio, which prevents people from understanding.
For instance, here's a real recording in a meeting room I recorded in India.
[recording].
Okay. He's the director of India. We agree it's very difficult to understand,
especially for the acoustic, for the recognizer to recognize a talk with lots of
background noise and interference like that.
So our goal is to separate the sources from the recorded signal, which is a
mixture. And this problem is known as a blend sort separation. It's BRS. And
BRS have loss of practical application, for instance, for hearing aid system, for
speech recognition, which is very familiar with you.
And so for like robotic or music information retrieval in this community we have
people who try to separate the different components like [inaudible] or speech
component to do some music information retrieval task.
So considering the recording environment, we in reality we have two types of
environment. One is [inaudible] and the other one is reverberant. What I say is
any [inaudible] environment come from the perfect studio or in the outer
recording where the [inaudible] environment come from a meeting room or to a
[inaudible].
For instance, if you record a mixture in any environment you will hear quite clear
sounds like this. [recording].
>> Ngoc Q.K. Duong: Main voice you can claim. But you can do the same thing
in [inaudible] with a lot of reverberation, what you will hear is this [recording].
>> Ngoc Q.K. Duong: Hear a lot of echo and you feel that this one is actually
very difficult to process. And why you have such differences is because in an
environment you only record [inaudible] from the source to the microphone
without any reflection, why in the reverse is true, you have a lot of sound
reflection from the source to the megaphone. So this is a nice picture from the
cafeteria in India.
So as you hear the sounds and you see from here it's very difficult to model
exactly the acoustic path from the source to the microphone in any reverse
environment. And the source separation here remain very challenging, why a
state-of-the-art profile already some good resource in the case of any good
environment.
That's why in my Ph.D. work I focus more on the modeling of [inaudible]
environment which get more practical application.
Okay. Now, if you look at some state-of-the-art process, there's two kinds of
information we can explore. The first one is to model and explore the spatial
information that is looking at the spatial position and location of the sources. And
another one is to model and explore the spectral cues which is more important to
the spectral information of the sources. More detail, as a spatial [inaudible] one
of spatial cues, you can image in this place and intensity differences.
For instance, you look at any recording environment and if the sort is here, which
is closer to the microphone I C1 so the signal I C1 will be larger than I C2. So
you'll have a very simple pro personal amplitude between I C2 and like that. If
the source move to the position B which is closer to microphone I C1, you have
the spectral cue now it's blue 1 B, so that ice 2 is larger than ice 1. So this is
very simple gives you the basic ID of the spatial cues, and for the spectral cues
you can explore, for instance, like if you look at the spectrum of speech, it can be
explored [inaudible] the smoothness, for instance, the spectrum here is very
smooth over the frequency reigns and it's capacity because here a lot of
[inaudible] point, the coefficient is close to zero. And if you look at the state of Art
for source separation we found there's much work on spectral cues that is based
on statistical model like GMM, HMM or non-negative metric factorization, for
instance, and there's actually very little work on spatial cues, and most of them
based on the [inaudible] model. For instance, in the [inaudible] recording and the
deterministic [inaudible] model is the source position by the face and intensity
differences.
We are far from the actual characteristic of the reverberant environment and also
for the diffuse background noise where you cannot model deterministically the
spatial information of the sources.
So for our Ph.D., looking at that problem, you have assist from the deterministic
model to the probabilistic model framework for spatial cues, that is our main
contribution. And then we design general architecture for model parameter
estimation and source separation.
And then we propose several probabilities prior over the spatial position of the
sources over the spectral information of the sources and [inaudible] the potential
for the proposed framework in various practical shaping that I'll show later on in
the simulation.
But here it's summarized of the contribution and I will address this problem later
on. Okay. So given that very general ideas and overview. So here will be the
contents of my presentation.
In the next part, I will focus on the general frameworks and parameterization
where [inaudible] propose general Gaussian modeling framework, spatial
co-variant parameterization and also source separation architecture EJ for
general case.
And then in the next part I move to the center of the problem is how to estimate
the model parameter, right? We have framework. We have parameterization,
but it's very important that we merge the parameter in order to perform our work,
then I will present several probabilities prior in order to help enhance source
separation. And finally I will come with some conclusion.
Okay. So now we look at the problem in a more mathematic way. We have to
formulate it right. So you have original sources it's denoted by X by J where J is
the sources in the patio room and what you observe at the microphone is not
actually the cell. It's a recorded signal [inaudible] and CJ is recorded source
images it means it's a contribution of the sources at the microphone.
And it's the proposed of source separation is that given the observed material
here, you will need to estimate the source indices CJ.
And since we have mixture of several sources, what you really observe at the
microphone array is a mixture it's called I sub T, I by one vector where I is the
number of microphone and IT would be the sum of TJ, J over 1 is the total
number of sources.
Okay. So now propose given XI you estimate the CJ. Okay. So let me
emphasize that. We are not getting estimate in the original sources but we try to
estimate the source indices.
Okay. So first ask of the modeling framework, most across I use deterministic
model for a spatial cue with realize on the two main assumptions. The first
assumption performance is pro source assumption where acoustic path from the
source microphone is modeled by the missing vector H sub J. So what you
observe at the microphone CJ will be the conclusion of the original sources with
the missing vector S sub J.
And then here is a convolution in time domain, if you assume that the window in
line is much larger than the actual hinterland of XJ you have a narrow band
approximation where the conclusion in time domain is approximated by the
complex value multiplication in the frequency domain.
So given those two basic assumptions, most set of the across view they're
source separation system. So we see that in practice these two equations do not
house due to a cup of reason, for instance do not say the SJ, so when I talk I'm
not straightforward like this, sometimes I move, sometimes I move my head. So
we cannot model by deterministic machine vector S sub J and also because of
diffuse reverberation sources. You have very diffuse, very lots of reverberation,
modeling by single missing vector may not be enough.
So for that reason we switch to probabilistic framework, and here it is. So in our
proposed framework, we propose to model the source indices CJ as zero mean
Gaussian random variable with the co-variant matrix is sigma J. And here is the
form of probability function for Gaussian, it's simple.
Let me emphasize a bit why we use the Gaussian modeling here. For instance,
in source separation, many people use Laplacian distribution for their sources or
something, but instead of Laplacian we use Gaussian here.
Couple of reasons for this, because first if you consider the physical acoustic, so
the reverberation is generally model extra Gaussian, is acoustic point of view.
And it is easy to handle the computation. So if later on I will show with the
Gaussian modeling we will just in a close-up date format for the
parameterization, which is good. We showed, of course, that it worked. So this
is a very important point.
Okay. So furthermore, now what you have is this one. This is -- you have zero
mean already, and you have unknown co-variant sigma A and furthermore in our
framework we factorize sigma A by two parameters VJ and IJ, where VJ is a time
variant source, variancies where we encode the spectral temporal of the spaces.
So if you [inaudible] so it's modeling spatial temporal power.
And IJ is actually we call it a spatial co-variant matrices where we encode the
spatial information of the sources, what we refer to spatial information, it will
include the spatial -- the spatial direction of the sources and the reverberation in
the room.
So both spatial information of the trusses is encoded here and all the spectral
information of the sources, for instance, it can be modeled by G and M and S and
M, for example, is coded by VJ, so you separate it by two components and all of
this is encoded in the spatial co-variant, in a co-variant matrix sigma A.
>>: Can you go back to the previous slide? So that the dimension of the vector
here is just frequency?
>> Ngoc Q.K. Duong: Vector here, C?
>>: You have N and F, when the matrix -- you're looking at frequency is the
dimension of the matrix?
>> Ngoc Q.K. Duong: No it's the dimension of the metric is in the -- it's the
number of microphone. So if you have two microphone, you have two-by-two
matrix. So you have a C here is a vector of the -- let's say I have I microphone.
So C is the vector of I by 1, right? So you have one source here. What you
observed at the I microphone is a vector I by 1.
>>: So all frequencies are, one frequency dependent on the next one, the
adjacent one, right?
>> Ngoc Q.K. Duong: No, not really. So here we model for -- each time
frequency independently.
>>: Right. That's what I'm saying. We're making the assumption that what
happens at this frequency, the next frequency, it's independent.
>> Ngoc Q.K. Duong: Yes.
>>: Sigma J is separate for each request but not [inaudible].
>> Ngoc Q.K. Duong: Yes, true, general or something. But later on when I come
back I'll make the less strict something where I can assume some dependencies
in terms of frequency point. But at this time it's for general framework let me
assume first that it is independent and let me model first for each frequency point
by this one.
Okay. So, again, V will be the scalar and R would be I by I, square matrix, where
I is the number of microphone. So if you have stereo case, you have two-by-two
microphone. For each time frequency point, N for sources J.
Is that clear or something? Okay. And in most of the following we will more
assume that IJ is time invariant. So we will not have time here. The reason we
assume that is, for instance, now we don't deal with some very challenging case
for moving source. So we assume more source utilization or [inaudible] so we
assume that IJ modeling the spatial information is time invariant. But also let me
come back to time varying case later in my presentation.
But at this point, okay, for that. So this assumption is assumed by most
state-of-the-art process, where the spatial location of the sources is modeled by
the missing vector, which is time invariance.
Okay. Okay. Let me -- so we'll hear, for instance, there's a model of the spatial
information by time invariant S dependent F. So now we make the same things
like this one.
Okay. So now as I said before, our work is mainly focussed on modeling the
spatial cues which means we focus on the model for IJ and the next slide I'll
present the parameterization for IJ.
Okay. So now again look at the state-of-the-art process for IJ in the inadequate
recording where there's no reverberation. So IJ can be computed directly from
the missing vector. Right? So, for instance, in the inadequate missing
environment, if you know the source and the microphone position, so the
knowledge from the room acoustic would allow you to compute directly the
missing vector from the source to the microphone like this, where here, I refer to
the N is the missing environment.
So if you compute IJ, analyze this one, so the co-variant metric I of J can be
computed like H and [inaudible] that is simply [inaudible] and why I refer to the
right one here, because this is the product of two vectors. So the metric is one,
one, metric. Okay.
If you look at the popular parameterization based on the narrow band
approximization I presented before we have CJ approximated by the product of
IJ and original sources.
So now if you compute the co-variant metrics of CJ, so you have sigma A,
expectation of CJ and CJ eight and you reduce in this form, why this part is
scalar and is VJ, it encodes a special temporal, spectral temporal information of
the sources, and the spatial co-variant metrics IJ can be computed by SJ. SJS.
And again it can be the 1-1 metrics. Right? So what I say in this slide is that
whatever you consider the inadequate recording environment or reverb
environment, the state of the S parameterization for IJ is the 1-1 matrix in both K.
So what we do is that we don't want the 1-1 matrix, we want more full rank matrix
with -- for more free parameter to better model the reverberation.
So we look at what we call here is the full rank direct diffuse parameterization
where we explore the knowledge from the room acoustic. This model is partly
new because it is considered -- it was considered in the context of source
localization before but the first time we look at it in the context of source
separation.
Okay. So if you assumed that the reject path from the source to the microphone
and the reverberation is uncorrelated, so the co-variant is the sum of the
co-variant of the direct path which is computed right here, by the missing vector.
And the co-variant of the diffuse reverberation path.
Okay. So the underlying assumption is that the [inaudible] and reverberation
path is uncorroborated, where SJ of NI is computed before.
So if you look at the state of the art. So state-of-the-art modeling is this one. So
if we look at a full ranked parameterization where we adhere some contribution of
the reverberation.
Okay.
>>: I have a question here about -- if you go back to the previous slide. So built
in the lower equation, right, some of your channel characteristics are now being
captured in the covariance only in the expectation, statistics over the expectation
of the inner product. That's going to lose something it's not the entire channel
characterization it's some characteristics, expectations. My question is when you
go to the next slide you're saying okay now we're going to open up this matrix to
be full rank, the matrix to be full rank, do you have some intuitions behind
covariance is a good means for capturing the reverberation channel
characteristics because it's not 100 percent. It's capturing it in expectation, what
do you lose in that presentation?
>> Ngoc Q.K. Duong: Okay. So what I said before is that for state of the art
most processes like deterministic model for spatial information by the missing
vector, so if you apply directly sky of deterministic model in our framework, so for
Russian modeling framework, this one, it's our proposed modeling framework.
And if you bring directly the state-of-the-art parameterization -- so you will get the
right one.
>>: I understand that part. But I get that. But what I'm saying is like here you're
saying that you're going to expand that by using full rank, right? But there's still
this question of why is the covariance structure the right way to represent
reverberation? Is there enough information there in the covariance to really tell
you about the reverb channels?
>>: Because the question, is it Gaussian or not. Because if it is then that's
probably fine. If it is. But maybe it isn't.
>>: I was wondering also what's being lost when you turn this into an expectation
quantity over ->>: But if it is Gaussian, then you're just many -- you should not be adding that
term. Maybe some other combination.
>>: That's right.
>>: But it may not be Gaussian, we don't know.
>>: Yes.
>> Ngoc Q.K. Duong: Okay. I will demonstrate -- I understand your question is
why we need the full rank and why we need to ask more parameterization in the
co-variant message.
>>: That's not really my question. It's okay. I can ask you later, too. That's okay.
Sorry. I'm really -- I'll say it again but you don't need to necessarily answer it
now. Maybe it will become clearer in your talk my question is the Gaussian a
good way -- is the Gaussian approximation a good approximation for what's
actually happening?
>> Ngoc Q.K. Duong: Okay. I would say Gaussian is the best way, it's a good
way. But as I point out several reasons why we consider Gaussian in previous
slide. Of course, you can consider another one, for instance, Laplacian or
something, but it may be more difficult for you to estimate the parameter later on
or something. But I haven't been doing this.
>>: My point is if it turns out that it's not very Gaussian, then adding more
parameters to a Gaussian representation won't necessarily help it. But if you
have a strong argument for why it is a Gaussian ->> Ngoc Q.K. Duong: Okay. Now I understand your question. But for sure, for
physical acoustic, if you look at the acoustic book, where most people in physical
acoustic, the community will model the reverberation as a Gaussian. I mean, not
modeling both as a Gaussian.
I mean, if you consider the reject path, it's okay, it's not Gaussian. But for diffuse
reverse path, they really model Gaussian. So that is one of the reasons we
consider.
>>: It's a staging -- this thing it passes from the walls where the speech signal
distribution basically moves from the sharper [inaudible] and more and more
Gaussian and there's the tail of yet this completely Gaussian. Pretty much an
infinite number of [inaudible] but the direct path and the tail kind of a -- goes from
the sharper distribution and this is what actually is missing there.
>> Ngoc Q.K. Duong: Yeah. I'm sorry for that. For example, if you look at the
modeling for the origin itself, for the S -- for -- okay. Let me come back to this
one. If you look at the modeling for the sort here, it's obviously not Gaussian. It's
more like lap lap or something, but now you're looking at the model for it's the
image to the microphone. There's a lot of reverberation, so there could be some
less sharper as evaluation.
>>: Okay. Thanks.
>> Ngoc Q.K. Duong: Now we stop here. And this model have been considered
in the context of source localization in 2003 for the first paper I saw.
It's now we bring this one in the context of source separation and we see how it
performs in this context.
>>: So the second matrix -- sorry.
>> Ngoc Q.K. Duong: So, yeah, if Z is something that is satisfied and if you
know that the [inaudible] is shutting, then you know everything. The knowledge
from the room acoustic will allow you to compute omega and sigma directly from
the room acoustic.
For instance, if the room is rectangular, if you know the reverbs abrasion
co-vacation you know the time and you know the area and so you compute the
proportion between the reverberation as it reaches the path and it's very nice that
this co-variant matches here. It's like a sync function. So, yeah, it's proved
already. So it's kind of deterministic. If you know everything, you have this
model.
>>: So the second -- all I could think is in 1954 paper I can't find it, I believe, what
did you get the second -- what did you get the second at?
>> Ngoc Q.K. Duong: This one?
>>: Yeah.
>> Ngoc Q.K. Duong: So from the textbook.
>>: Okay.
>> Ngoc Q.K. Duong: It's a very old textbook like the '60s or something in its
proof already. And this equation is so written -- it's my mistake, I should mention
some reference here. In Marco Wire [inaudible] in informing.
>>: I think his paper [inaudible] it's the second, I think.
>> Ngoc Q.K. Duong: Micro Wire so easy to model ->>: That's earlier paper. The 1954 is the complication of the [indiscernible]
governance matrix, but no one uses it.
>> Ngoc Q.K. Duong: That's why it's not really new but it's new in the context of
source separation. I consider it here. But really this is not what I want.
I just move from the ring one to the one I want. So what I really want is that here
you see that it is full rank. But these two must constrain, you have to know
everything and this contribution of this part and this contribution in this part is too
much constrained.
And what we want is we want to relax all the constraints and we want to present
IJ as really a full rank matrices. Okay. So what this looks like.
If you consider state-of-the-art rank one where rank one [inaudible] or rank one
convoluted, the co-variant -- the spatial co-variant mate trick is a product of two
vectors. We say 1-1 matrix. What I propose in my work we propose to present
IJ with a homogenous message where we release all the constraints. So you
see that over slides. This one is too much constraint. It's less constrained. We
ask more. And this one is what we propose here. It's really unconstrained.
So we have more parameter to model through reverberation. Okay. So now we
already have Gaussian modeling framework. We have parameterization for the
spatial co-variant matrix, and it's time to reside the source separation
architecture.
Okay. Now look at it. You have observed what's I sub T you transfer into the
time considered domain you have ice NF. Given the Gaussian framework, it's a
parameter you need to estimate is source variances for each sources and the
spatial co-variant matrix for its source array. And once you estimate this one you
can perform monkey channel [inaudible] to estimate C of J and then you
converse back to time domain to get what we want.
Okay. For multi-channel filtering, if you have an equation here, if you know VJ
and IJ for all time frequency points, for all sources, right, so you -- okay. So this
is simply an equation. But here let me emphasize that here we assume that the
sources is uncorrelated.
So we have a co-variant matrix of X is the sum of the co-variant message of each
sources. So this is uncorrelated assumption which is less than the
independencies, so this part and this part is ready. What we want now is this
part. How we estimate VJ and IJ.
Okay. This will be our focus. Okay. But before actually estimating this
parameter, let me first demo and show the potential of the proposed framework
in article strapping and semi blend setting.
For instance, in the Oracle parameter estimation all the parameter here is
estimated from the known sort in this. So this means that this will provide the
upper bounds of the source separation performance. If you know everything and
you can compute parameter, it will show you the upper bound.
So I just want to prove that upper bound on source separation of the proposed
framework is higher than the upper bound of the performance of the state of the
art across. So if we succeed in this way. So later on we will manage to estimate
the parameter blindly for the parameter. So that is the proposal of this work.
And in the semi blend, because semi blend parameterization, it means we
estimate the spacial parameter from the known source images but we blindly
blend it from the source parameter.
So I will skip the detail and present later on. But that parameter is estimated in
the maximum likelihood, using EM expectation maximization algorithm.
And we evaluate the performance, the source separation performance using the
well-known criteria like signal to distortion SDR. And signal to interference ratio
or something.
Are you familiar with this iteration matches?
>>: The signal distortion issue and [inaudible] factorization.
>> Ngoc Q.K. Duong: Okay. So for this criteria if you have the estimated signal,
so say that estimated signal can be factorized by the sum of several
components. So you have estimated signal, maybe the sum of the original
signal, plus some artifact, plus the interference from other sources. Right?
So we have several components. So the signal to interference ratio, we mean
the ratio between the two source signals and the contribution of other sources
which is in factorization. And signal to distortion ratio we have the range of the
overall distortion. It's the range of the good sources to all the other distortion.
And the signal to artifact will measure the ratio between the signal and the artifact
and the musical noise for instance. So you see SDR we measure the overall
performance of the system. Why this we measure the specific application.
>>: So you're trying to estimate the actual signal or a filter version of the signal?
>> Ngoc Q.K. Duong: A filter version of the signal.
>>: I have a question of the number of parameters here. So the covariance
metrics it's full rank and full constraint. N squared over 2 parameters for each
covariance matrix, right? And then you have that separately for each frequency
band, right?
>> Ngoc Q.K. Duong: I get -- I'll prove that later on in my slides. Thank you for
that. Okay. Yeah. So as I said this is well known. So here is the resource in
two case. This is the average for ten speed [inaudible] resources with the
different UI, and the microphone spacing we use is 20-centimeter from the
distance from the source to the microphone is 1.2 meter. And we compare the
resource of our proposed full rank unconstrained parameterization with the full
rank direct [inaudible] partly new as I presented before. And we compare with
the state-of-the-art rank one convoluted and rank one inequitable model and we
compare with the two baseline across. This is well known. It's called Valerie
masking and L norm minimization. And this is the resource we have.
Regarding your question about the number of parameter. So, of course, you see
for the full rank unconstrained you have maximum parameter than another one,
right, because you have three parameters for each sources. Each time
frequency point. So if you multiply by the number of time frequency point and
you multiply by the number of sources, three, you get this total number of
parameter, need to be estimate.
For rank one convoluted, which is mostly used, we have half a parameter,
because this is rank one so there's only two. And it's very interesting that for
rank 1 diffuse two you have very little parameter.
>>: Rank 1 would be the square root, right? This is -- the 3,000 is that coming
from the filter length of the convoluted, the estimation of the convoluted filter?
Because I mean if you have a rank one matrix versus full rank matrix, the square
root, the number of parameters, right, not half? Rank one is just a vector ->> Ngoc Q.K. Duong: Okay. Now you consider the status of ->>: When you say convoluted, is that the number of filter taps that you're
estimating for the filter response, or why is it so large?
>> Ngoc Q.K. Duong: No, no, okay, for instance, here I use 1,024 taps for the
filter. So we need to estimate positive half of that, right? So this would be 513, is
the number of frequency band, right? So we multiply 513 with the three sources,
multiply by three. And if this true stereo case, you have two-by-one vector for
each missing metrics. So it's 513 multiplied by three, multiplied by two and we
get this number and for the full rank you get that.
>>: How many microphones?
>> Ngoc Q.K. Duong: Two microphones are used.
>>: So is this a real recording or it's a simulated?
>> Ngoc Q.K. Duong: It is simulated.
>>: And using image methods?
>> Ngoc Q.K. Duong: Yes, I am imagine method.
>>: Up to the 60 the room ->> Ngoc Q.K. Duong: It is 250.
>>: Okay.
>> Ngoc Q.K. Duong: Yeah.
>>: What's the sampling rate for this.
>> Ngoc Q.K. Duong: It's 16 Q Herz.
>>: How long our reverberation can you handle with a thousand taps assuming
the limitation of the product?
>> Ngoc Q.K. Duong: Okay. So for 16,000 and now you have only 1,000
depths, so it's like one -- 16 or so.
>>: 57 seconds.
>>: Much less than 250.
>>: So you pass the one derivation goes down, and DB and explains the best
numbers there.
>> Ngoc Q.K. Duong: Okay. Again, so I have something. So if you have -- we
have 16 ->>: 16 kilohertz. 1,000 frames. It's 16 of a second which is 87. 86.66
milliseconds. This is roughly ->> Ngoc Q.K. Duong: Okay.
>>: It's what you have is the 16. Which is where the derivation goes down to
minus 60 degrees. So mature, taking the stand of the reverberation where it
goes down to minus 20.
>> Ngoc Q.K. Duong: That's our proposal because we need to take the short
filter compared to the actual reverberation if you take it has no meaning.
>>: If you have [inaudible].
>> Ngoc Q.K. Duong: Misunderstanding here.
>>: Work on it anymore.
>> Ngoc Q.K. Duong: Okay. So, yeah, here is the resource for Oracle. For
Oracle, of course, you have a much larger number because everything is
estimated from the known sort images and the separation performance is the
degree in a semi blend but overall you can see the proposed full rank
unconstrained outperform another.
>>: So you said that your matrices were number of microphones, the number of
microphones. Here they're just two-by-two.
>> Ngoc Q.K. Duong: Yeah.
>>: So then -- then the explosion parameter is very small, because N squared is
just four. As opposed to like if you had ten mics. So I wonder, so I'm just
wondering, because so could you actually break down the 46, 17, where those
parameters are coming from, where the 46 / 17 are coming from for the rank
case.
>> Ngoc Q.K. Duong: For the full microphone case.
>>: No, no, just for your case, just want to know the breakdown of 4617 matrix of
where those parameters are coming from.
>> Ngoc Q.K. Duong: In terms of a spatial parameter?
>>: Just what are the -- because you broke it down for the rank one, convoluted
one you said 512 tops, times ->> Ngoc Q.K. Duong: You want ->>: In this case.
>> Ngoc Q.K. Duong: Okay. So for this one, we also have 513 frequency band.
And you also have three sources. Let me emphasize that. We are focusing on
the undetermined case where we use smaller number of microphone to separate
larger number of sources, which is much more challenging.
Okay. So that's why I used stereo for three sources. So let's come back. You
have 513. You multiply by three. And you multiply by four for each point.
So you have that. But what we really are happy and surprising is that for this
model with very little parameter, but it provided quite good resource is a bit less
than the state of the art here, but it used very little.
Let me explain why it is eight. For instance, if you look at here, so what you need
to know is that microphone spacing is one parameter. And you need to know the
distance from the source to the microphone. So if you have two microphones
and three sources, you have six parameters, right? You have six parameter for
the distance and microphone spacing is seven.
And then you immediate to know a bit about reverberation time, and that's this.
>>: So are you estimating the room parameters as well in those figures?
>> Ngoc Q.K. Duong: No. For that I used -- I assumed that it is known. Yeah.
>>: But you couldn't estimate those in principle.
>> Ngoc Q.K. Duong: That is one of the pieces of work I would mention, yeah. It
would be nice if we can estimate the parameter and incorporate it, yeah. But at
this time let me first -- I should assume we know ->>: So actually if you look at the upper table, the full rank unconstrained, the full
rank by diffuse are fairly close. It's only when you do the estimation.
>> Ngoc Q.K. Duong: Yeah, yeah.
>>: That all of them --
>> Ngoc Q.K. Duong: Yeah. That is really amazing. It means that if we know
exactly everything. So this model is this quite good to handle the reverberation
part.
>>: Even before you maybe do this future work of trying to estimate those, it
might be interesting just to see what the sensitivity of those results would be with
respect to small perturbations in the room estimate. Because if it's robust to ->> Ngoc Q.K. Duong: I see what you mean. When I presented at some
conference some people asked me about the variation about that. To explain
that. But for a short time of my thesis actually I haven't got much time to
investigate this one. I'm more investigating this one because in France we have
almost two and a half years for doing research and a half year to write a thesis.
So actually for me I only have two years to do those things. This is shorter than
in the U.S. But you're right.
Okay. Let me continue something. So now I proved that for the upper bound on
the source separation you have good performance. So let's move to the real
parameter estimate.
>>: We don't want to hear ourselves then?
>> Ngoc Q.K. Duong: Okay. Nice. [laughter] we have like 15 minutes more.
Okay. Nice.
Okay. Here is just one specific case. I did a long time before. But recently I
write my thesis so I test on a very large database and we get similar ones with
different sort of microphone different duration time. They're all there and so I
get -- for instance, you have this [recording].
Okay. There's three sources. And for the right one convoluted K, state of the art,
one voice. [recording].
Okay. And in our case you hear. [recording] okay. Again. [recording].
>>: Full rank in the thesis.
>> Ngoc Q.K. Duong: Okay. Yeah, you have more. [recording].
So in this, you have lots of physical noise, right? There's artifact. That's why we
use SAR, and you have more musical noise.
>>: So in the Oracle results, what you mean by Oracle is just the geometry.
>> Ngoc Q.K. Duong: It means we know everything, we know the source.
>>: You know the whole signal.
>> Ngoc Q.K. Duong: We know the whole signal, yes.
>>: Not just signals. [laughter].
>> Ngoc Q.K. Duong: It will give upper bounds of performance.
>>: I know the signals.
>> Ngoc Q.K. Duong: Okay. [laughter]. That's why I didn't want to place out
here because I know everything. So just know where to put it out here. But I just
want to prove if the parameter is estimated from the very good -- I mean, this is
known. So we prove that.
>>: Lower case the geometry is known but not the source images, right?
>> Ngoc Q.K. Duong: Yeah, yeah. Now ->>: I have one question about this. Your figures of merit do they depend on
frequency as well?
>> Ngoc Q.K. Duong: Yeah.
>>: It seemed like for the full rank unconstrained, most of the signal to -- most of
the interference was low frequency.
>> Ngoc Q.K. Duong: Yeah.
>>: That there wasn't a lot of leakage of high frequency from the other sources.
>> Ngoc Q.K. Duong: Uh-huh.
>>: Is that -- why would it -- first of all, is that truly happening, and why would
that -- what's causing that? Why would the low frequency leak more than the
high frequencies from the interfering sources?
>> Ngoc Q.K. Duong: Of course for the speech sources most of the energy of
the sources would lie in the low frequency, right? So, of course, in the low
frequency range you have more interference. I mean, you can hear more
interference. Because actually it's a mixture itself. It would have more energy
lying in the low frequency range, right?
And in terms of mathematical things I don't see the differences in my framework.
The differences with the low and the high, because we treat the low and the high
equally, and we apply the same parameterization for the old frequency mean.
>>: The interference sounds for when you played the full rank unconstrained
weren't a low volume male speech, it was a muffled male speech where the low
frequencies were leaking through. And so you have a look into what could be
causing that in your framework or --
>> Ngoc Q.K. Duong: Yes, actually I didn't really look closely inside the
spectrum feature. Does that really affect the speech recognition system or
something?
>>: Yeah.
>> Ngoc Q.K. Duong: Okay. Okay. Thank you for that. I will look at more or
maybe it is just one specific case, because we have three sources and I play only
one sources.
When you hear another source maybe it's different, or different sources, I don't
know. But for this I feel equally.
>>: I guess similar thought. How much is the difference -- maybe you haven't
done this analysis but particular spacing, you know, is going to make some
differences then, make -- you are not going to have the same estimation
capabilities for different frequencies given a different aperture. That might be
where the limitations are coming from.
>>: Either that or the framework ->>: Yeah, exactly.
>> Ngoc Q.K. Duong: For that frequency solution, let me present in this slide,
because I also have some work on the frequency resolution where instead of
trying [inaudible] form we provide a linear resolution I use some more like
acoustically motivated representation we provide more resolution at the low
frequency range.
I'll present later on in this work. So let me move. Okay. So now we move to the
next part where I present general framework to estimate the parameter from the
mixture.
Okay. Here is the structure. I choose expectation maximization EM. It is well
known for the Gaussian mixture model. And for YEM [phonetic], you may know
that it's very sensitive to the initialization. So we need to design a good
parameterization initialization scheme. And in the maximum likelihood, since we
measure it independently in the frequency mean, so there may be some
permutation problem in the domain, so later on we need to show the permutation
problem..
So what is new in this framework is that in most signal processing processes, so
the input for the parameter estimation is of the signal ice. But in our case we
consider the input by the empirical mixture co-variant sigma of X is that of the
signal itself.
So I will explain this one later. But now here we have several block ices for the
bland parameter estimation and we also consider the parameter estimation in the
maximum posterior sense where, okay, there's a mathematical term. And M this
case if we have some prior knowledge about the parameter.
So we can estimate the parameter jolly [phonetic] in this so we don't need to
show parameterization problem. So this is the general block. And following I will
present in detail in each step.
And for these two steps, I just explore the existing methods which is not our main
contribution. And our main work we focus on these three parts.
So here is the parameter initialization. I mainly rely on the work of Winther
[phonetic] presented in [inaudible], where he tries hierarchical clustering of the
mixture at each frequency mean after some [inaudible] and amplitude
normalization. So for the source of time let me skip this slide because it's not our
main contribution, it's just for parameter initialization.
Okay. I'll explain more about the empirical mixture co-variant, why we use input
is sigma hat of X instead of the signal itself. So, okay, I believe we need to
estimate VJ and IJ using this relation, sigma X. But in practice sigma X is not
observed. What we really observe is the empirical mixture co-variant sigma hat
of ice. And we compute sigma S of hat as the average over the neighboring
frequency point like this one. So and this one can be interpreted as [inaudible].
Later on I will present the resource with the equivalent rectangular bandwidth.
This is more acoustically motivated time representation. And why we want to
estimate the parameter from sigma X instead of the signal itself because
compared to iso sigma X, it will provide information about the interchannel
coefficient and it will take into account the neighboring frequency as you
mentioned before.
So we slice this and rely on the neighboring frequency point.
>>: Wait. Go back. So you're mixing between neighboring channels and
neighboring specs here is that what you're saying.
>> Ngoc Q.K. Duong: Not channel. But time frequency reason only.
>>: No, I understand. But time frequency regions.
>> Ngoc Q.K. Duong: Yeah.
>>: So this is time N and this is frequency. So give the same frequency being
back in one more back.
>> Ngoc Q.K. Duong: Yeah.
>>: And previous frame give plus the two neighbor frequencies.
>> Ngoc Q.K. Duong: Yeah. In the general case. If you set the length of that
two is two. So you have two-by-two. And I test several cases with different
length of [inaudible] and two-by-two I realize provides the best performance. We
said okay.
This one is the main point and this will one will contribute half of that. So you
have a shape of filter. Okay. And here's your general expectation maximization
algorithm. It includes N step and M step. In each step we try to estimate the
multi-channel [inaudible] and the estimate co-variant for each sources, sigma FJ.
I will skip the detail. And for M step, the parameter is the iteratively update, like
this one. VJ and IJ. So update of VJ will depend on IJ and update IJ will depend
on VJ. This is a maximum likelihood sense. And in the maximum post
[inaudible] VJ and IJ can be estimated by the co-sponsored including the
contribution of the likelihood and the contribution of the prior which I will present
later on, where I introduce some [inaudible] parameter to take into account ->>: You estimate both these NPRs simultaneously?
>> Ngoc Q.K. Duong: Yeah, because we don't know these two parameters,
right? Yeah.
>>: From the same amount of data.
>> Ngoc Q.K. Duong: Yes, from the same amount of data.
>>: Because the V in theory you could learn with a lot more data, nothing
specialized right?
>> Ngoc Q.K. Duong: Yes, I see. There's many -- processes learn VJ. But to
learn VJ you need to know -- I mean the training data should be close to the
isolated data. But, for instance, in source separation context general case when
some people go into a room and talk you don't really have training data.
And also in state of the art many models for VJ is present like you can present VJ
at NMF model or mixture of some Gaussian. And they will train the Gaussian
mixture model to get the estimation of VJ.
But here, because my framework is focused on IJ. So we assume that there's no
prior information on VJ.
>>: But VJ is a bunch of M and F. So it's like a ton of parameters, right?
>> Ngoc Q.K. Duong: Uh-huh.
>>: As long as they are trans length?
>> Ngoc Q.K. Duong: Yes. If you do not put any prior information, yes, it has a
tons of parameters. But if you put some model for VJ, for instance, in MF order
so you have VJ would be some activation and some pattern, some pattern, for
instance. So you have less parameter.
>>: Are you doing this utilization separate than for --
>> Ngoc Q.K. Duong: Yes, it is doing separately for each sources. Each
frequency.
>>: But not each frame. You're doing this tied across the entire input.
>> Ngoc Q.K. Duong: Yes, because you see here R would be the sum of O
frame for VJ. Yeah. Okay. Is that okay? Yes. So for permutation problem, let
me skip, because I just reproduce the work of [inaudible] in Japan where he
explored the DOA, the direct -- the source iteration to sole permutation problem.
Okay. So here is some results we get. So this is the actual results. We also
average SDR, which measures overall distortion over 10 simulated speed
mixture.
So we compare the results of the full rank unconstrained with the rank one
convoluted case and the baseline across is by remasking L1 minimization
because at this time we don't take into account another model like full rank
[inaudible] because we already proved that it provided lower upper bound
performance. So at this state of the research I only consider the full rank
unconstrained. And here is the results for very low reverberation time of 50
millisecond.
So you will see for low reverberation as rank 1 convoluted and full rank profile it
leads to the same results because it's very low. But as far as we move to the
higher reverberated room. So output proposed parameterization will clearly
outperform the baseline across and the baseline across.
>>: Is it resource [inaudible].
>> Ngoc Q.K. Duong: No, it's really blocking.
>>: Static source locations or are they moving?.
>> Ngoc Q.K. Duong: Source location is fixed, but we don't know. Yeah. For
instance, now you hear the sounds. In 250 millisecond. [recording].
So rank one. [recording].
Okay. For our proposed part. [recording].
>>: I thought I heard results from the rank one convoluted mixture that is some
better than this.
>> Ngoc Q.K. Duong: In terms of?
>>: From other researchers.
>> Ngoc Q.K. Duong: In terms of interference or artifact or overall?
>>: Overall.
>> Ngoc Q.K. Duong: Okay. We can hear again. [recording].
>>: Just my recollection of some companies here ->>: Maybe they weren't in a reverberant room.
>>: That's probably the biggest difference, yes.
>>: So which depends ->>: How reverberant.
>>: Go back one second, what level were you showing those samples at?
>> Ngoc Q.K. Duong: 2,000 -- I'm sorry, 250.
>>: Okay.
>>: So maybe that's the difference, yes. It's possible.
>> Ngoc Q.K. Duong: But even for this one, I tested in many cases, full rank
clearly mattered. I don't know.
>>: I'm saying what I've heard in other conferences, the separation was much
better but perhaps it was much less reverberation.
>> Ngoc Q.K. Duong: Yeah.
>>: Because there they look almost the same.
>> Ngoc Q.K. Duong: In low reverberation time it's almost the same. But as I
said before, our result is getting the I for the reverberated environment.
>>: But compare that with lower reverberation times you do as well as ours.
>> Ngoc Q.K. Duong: Yes. Or even recently I test for the thesis I test a larger
number of datasets with different scenario. So at the time I observed that even
the rank 1 performed better at the low reverberation time.
>>: It was even better than 10 DB. Maybe 50 milliseconds better than 10 DB.
That's my recollection.
>>: 17.
>>: I'm sorry?
>>: 17. You said [inaudible] this is what they used when they --
>>: Like the guys from ATR, the demos I listened to, to me they sound better
than 10 DB. I know that reverberation is ->>: They have different definitions.
>>: Did you use headphones when you listened to them?
>>: I tried both.
>> Ngoc Q.K. Duong: Okay. So this is one case.
>>: I have a question for the room. Was it -- I'm not familiar with the data you're
using for this. And to me both examples sounded unintelligible. I was maybe
able to pick out two or three words from either the rank 1 convoluted or the full
rank unconstrained. So it doesn't really seem like the difference is useful at 250.
Is this the biggest difference that you see with this technique, or are we going to
see better results?
>> Ngoc Q.K. Duong: Yes, if you look at the number, you do see differences but
here as I mentioned as I display one specific case.
>>: Here I see 2 DB difference at 250 milliseconds.
>> Ngoc Q.K. Duong: Okay. It's like one DB or something.
>>: One DB. Quantitatively they're different but qualitatively I found them to be
both be unintelligible. Do you have some experience that shows that there's
some domain where you use this technique and there's qualitative results that
are positive?
>> Ngoc Q.K. Duong: Okay. I will show you later on. But let me emphasize
that. In source separation community, one DBSDR is really a last improvement.
If you look at the performance year after year. So we see that it's a process like
1.3 or 1.5 FDR or something performance, so it's not easy to get like one DB.
>>: This is a significant change.
>> Ngoc Q.K. Duong: Yeah, yeah. Let me emphasize that this is really a
significant change. And in this slide I saw some more and resources compared
with state-of-the-art across. So in source separation community, we have a
campaign which is organized by one and a half years by the steering committee,
associated with the source separation conference, which is known as the
[inaudible] conference.
And for this campaign we are the organizer have some common data, and the
participant will use their algorithm to separate the file and submit the results so
that the organizer will evaluate the performance. So they give the blind data. So
all the participants don't know anything, and they give back the wave file and the
result is evaluated by the organizer.
And we participated in the data 2000 -- recently it's 2010 already, and we
compared with five -- state-of-the-art process, for instance, [inaudible] came from
an entity in Japan, well known for source separation and many of them come
from Columbia University with Dan Ellis, so very famous and [inaudible] came
from Tokyo University. So it's all state-of-the-art process. And here I test with
five microphones based datasets and here's the results we have, with three
sources and two sources compared to state-of-the-art process.
>>: So that was the number of the entries? Because of those number?
>> Ngoc Q.K. Duong: Yeah. I compared to all the numbers.
>>: 250 millisecond it looks like the key method is 3.7 versus your 3.8. It's close
to ->> Ngoc Q.K. Duong: Here?
>>: Yeah.
>> Ngoc Q.K. Duong: Yeah, sure. I don't [inaudible] with that I outperform
everything. This is really hard. And let me also emphasize that CDs with five
meter spacing and with less number of microphones facing even outperform our
methods because our method we need to solve permutation problem.
If you have large microphone distance, so you have many face wrapping, so it
will degrade a lot of performance, yeah.
So that's why I choose five-centimeter. But so the permutation is not the main
goal of our process.
>>: So your implementations of their algorithms or this is what they published?
>> Ngoc Q.K. Duong: Yeah, yeah, and the data is tested and submitted
themselves, not mine. I mean we all submitted to the same organizer. So that's
another thing.
And actually recently we were in 2010 I also attend and I didn't write resources
here but let me summarize.
In 2010 the group of entities over there outperform another one. And there is two
other people outperform this method. One from EPIPI Switzerland and one is
LSA but these two people use our framework. That means that he used exactly
the full rank I proposed here in 2009.
But he have more constraint on the source variances. So here the source variant
is free. I don't use any more VSA but for those two across, they [inaudible] mode
of VSA and Gaussian model for VSA and they get better performance. So it's
usual. Yeah.
>>: So one other question you may have said this before, but in all these cases
the number of sources is known, right.
>> Ngoc Q.K. Duong: Yeah, sure.
>>: It's always specified.
>> Ngoc Q.K. Duong: Yes. For estimating the number of sorts is remaining
challenge I think.
>>: But in all these experiments ->> Ngoc Q.K. Duong: It's known. Okay. So regarding the question about the
frequency solution before. I test between the certain full array presentation
where the frequency bandwidth is linearly equal for all frequency ranges. And if
you apply EIB, which is more acoustically motivated, it will provide narrower band
at the low frequency rate, where most cell energy lie in.
And our resources show that the EIB will perform better performance than the
software full array transform, why we have this because, yeah, so the difficulty of
estimating the model parameter is that we have a lot of time frequency overlap
between sources.
I mean, if the sources is really spare in the time frequency region, it is easier to
estimate the parameter, right? But if it's really overlap -- so it is more difficult to
estimate model parameter. But if you use EIB, we have a narrower band at the
low frequency range. So we have less overlap.
That's why it outperforms the certain for array transform and these results were
published in our ICI paper in 2010. Okay. There is PP.
And now for a short time I'll move quickly to also a good contribution of the paper
is defining some probabilities prior. Up to now I just present a general framework
as a parameter is estimated in the maximum likelihood sense, without knowing
anything. Right? But in practice, in many cases, for instance, if you look at the
speed enhancement in your car you may know exactly the position of the driver
and the co-driver. Or in a formal meeting, too, the position of its delegate is
fixed. It means that in such situations the geometric is known. So that you can
explore this knowledge in order to enhance source separation.
So as far as that motivation, we design the spatial location prior. Okay. Let me
also consider another one. So up to now I just assume that IJ of F is this time
invariant. But if you consider the moving sources, for instance, if I talk like this, I
keep moving. Or if you consider the run, so a separate run like he had in there,
so IJ should not be time invariant, right?
So in that time, we should consider time varying spatial position of the sources,
but we can design some continuity prior. It means that we assume that it's time
varying, but it should have some structure over time.
So that's why we use reside some space continuity prior for us and these two
different prior is published in two different ICAS papers this year.
Okay. Or if you look at spectral information of the sources, for instance, if you
look at spectrum of the room, it's quite mostly over time. Why if you look at a
spectrum of harmonics, a piano, it describes harmonicity over smooth frequency
range. And given that you can also design some spectral continuity prior to
enforce the smoothness over time of frequency range.
So these are a series of prior information we consider in order to enhance sort
separation in specific setting where we know something.
We detailed about spatial prior. So here is the model you have seen before. The
full rank diffuse [inaudible] but this model, we test with large data and we found
that it's quite good in terms of the operation fro the mean for the spatial co-variant
methods. It means that if you have a lot of personal sources, the mean can
follow this one.
But in practice, it will vary over the mean. That's why we can define some
distribution of IJ by the inverse we set prior where the mean of IJ is defined by
this, and we need to estimate or to learn the variant.
So that we know the distribution and we can estimate the parameter is the
maximum post [inaudible] sense, right? Let me go a little bit faster and just give
you a basic idea. And also we get close form update in MAPSIN. And here is
some results.
Here I just want to show that we -- if we know some knowledge about the
geometric setting we can get better performance, compared to the blind
initialization in a maximum likelihood sense, right?
Okay. For spatial continuity prior, we consider this prior in the context of musical
sort separation, where the music -- okay. And we are [inaudible] some property
distribution IJ. So the mean at the current time frame depends on the value at
the previous time frame. So we have continuity constraints.
So now I come back with experience to show some practical where our
framework is shown to provide good performance. For instance, if you look at
music mixture. So it can be considered as a mixture of harmonic component and
[inaudible] component and [inaudible] in the mirror community people try to
separate harmonic component and drum component in order to perform some
other music information retrieval, and we apply our framework with the continuity
prior, so we get results for multi-channel harmonic and focus separation and we
compare this result with existing single channel SPS which is proposed by the
group in the University of Tokyo.
Okay. And here is the results we get. Here is the, for example, one music
mixture. [music].
Okay. So here is the harmonic component, we separate. [music].
Here's focussing component. [music].
Okay. If you compare with state-of-the-art for focusing you will hear [music].
So a few differences now. Because our last question is I -- for speed it's difficult.
But I have some co-work with a group at the University of Tokyo where we tried
to explore this framework in the context of music information retrieval. Yeah.
So here instead of the when you hear loss of artifact, so the RAM is mass
resource, you may not hear the actual one I play again. [music].
>>: That might not be the important thing. The goal you're trying to find features
for mirror kind of stuff you might care about tempo and which [inaudible] and stuff
like that. The actual acoustic artifacts are if humans are listening to the output.
Another question I have in this case -- are you manually defining what the priors
are for the different types of sources here or are you estimating them from data?
Or where are they coming from?
>> Ngoc Q.K. Duong: For the prior, there's only two parameters. One is mean.
And one is variant. So for mean it's okay. It's well defined and for variant, I
manually choose it.
>>: Okay.
>> Ngoc Q.K. Duong: But I observe that the reason it's not very sensitive to the
two of the variant.
>>: One extent ->> Ngoc Q.K. Duong: Yeah. So it varies between 10 and 100, it's okay. But of
course, okay, we can learn from training data.
>>: The source is regular state of recording?
>> Ngoc Q.K. Duong: Stereo recording.
>>: Stereo or mono phonic, single channel.
>> Ngoc Q.K. Duong: For single channel we separate the source in each stereo
channel separately.
>>: So you did like, you took one of the stereo channels and then for each of the
results?
>> Ngoc Q.K. Duong: Yeah. So this is not a fair comparison, I will say, because
I compared the multi-channel.
>>: The single channel. The one is the multi-channel.
>> Ngoc Q.K. Duong: I will say it's not fair but for state-of-the-art process I didn't
use any multi-channel process, because for music separation, most people see
the channel and they explore the mode for the spatial temporal of the sources in
order to separate like.
So, yeah, I tried to look for the state-of-the-art multi-channel, but I didn't see one.
Okay. So here's the conclusion. So in this work we introduced probabilistic
spatial model for the reverberation and diffuse sources.
And we propose unconstrained parameterization of the spatial co-variant
matches which overcomes the narrow band assumption to a certain extent, and
we better account for the reverberation as shown in the experimental research.
We consider the local and empirical co-variant for the parameterization. It's
sigma hat of S which we provide additional information.
And recently we proposed several probabilistic priors which have enhanced the
separation in a certain context, where we know some information, yeah.
Okay. For future works, we can consider the work that was blind source
separation explored the spatial location prior. It's very related to the question
before where the full rank [inaudible] diffuse model. And even for this prior we
need to know the mean. It means we need to know that matrices and if we can
find a way to estimate the parameter like estimate the source UA and derivation
time it's smooth like this. And we can consider the use of the proposed
framework in -- another field of signal processing. For instance, in a mirror, that
is what we are doing now. And recently I found that there's some people already
use our framework. For instance, Hitachi, told me Hitachi use our modeling in
their acoustic canceling system and Anarchi [phonetic] also combined our
process with the time frequency masking. So to enhance sort separation.
>>: Is this [inaudible] 2011 paper?
>> Ngoc Q.K. Duong: Yeah. Because these two guys from industry. So they
consider the practical application. So so-called use the ID but he do not use the
same estimation technique because ours requires more time.
So combined with the process and used sort, faster estimation parameter. And
we also can consider the proposed framework in spatial audio where we
annualized and run the space [inaudible], yeah. Okay. And I think that is the end
of my presentation. And here are some references you can see.
>> Ivan Tashev: Any more questions?
>> Ngoc Q.K. Duong: Thank you very much.
[applause].
>> Ngoc Q.K. Duong: Thank you very much for your attention.