Přepis řeči - RESOLVING FD-BSS PERMUTATION FOR ARBITRARY ARRAY IN PRESENCE OF SPATIAL ALIASING

0:00:14	a morning everyone so um
0:00:16	yeah even here from the intelligent robotic on number to read john and
0:00:20	that would present this
0:00:22	so
0:00:23	first this is just was introduction so we are interested in
0:00:26	separation problem like co but party problem where
0:00:30	so were a speaker are talking and there's a microphone array
0:00:33	so we we
0:00:34	consider
0:00:35	blind source separation
0:00:36	in the frequency domain
0:00:38	and we are in the permutation problem
0:00:41	and especially in the approach based on the direction of arrival so from which direction the signal coming
0:00:47	and a
0:00:48	we focus on the special i'm guessing
0:00:50	so what we it do we we show some model using the special a yeah thing
0:00:53	that we can maybe have some sparse solution and have to relate to this
0:00:58	the the permutation resolution problem
0:01:01	so this is a line of the talk so first us would talk about the
0:01:04	frequency domain blind signal separation
0:01:08	then
0:01:08	then the permutation problem
0:01:10	and after that that will go to talk about the mess with base
0:01:14	do you rate estimation
0:01:19	and the proposed approach so the specially in in equation of finding a solution and how to relate to the
0:01:24	permutation with
0:01:28	so first a domain mixtures so this is there is
0:01:31	very fast to tree so we have to
0:01:33	to people talking in front of the microphone array in the time domain to comparative mixture
0:01:38	if we you the frequency domain we have several set of
0:01:42	uh instantaneous mixture so here it was a future here we have much we see so we have a much
0:01:46	we see that give us
0:01:48	mixed to a mixed signal in each of the frequency bins
0:01:53	so
0:01:54	but still separation in one frequency bin is just finding actually a metrics that we
0:01:59	separate so weak over the signal so green and red here from the blue
0:02:03	one of the problem is that actually
0:02:05	when we do we
0:02:06	when we this is
0:02:07	using a
0:02:10	statistical independence like
0:02:12	independent component analysis
0:02:15	we have the permutation problem meetings that
0:02:18	we don't know
0:02:19	the mixed are so we don't know the order of the signal when we equal
0:02:24	a problem is that in uh
0:02:25	a domain approach
0:02:27	when we do all the processing so
0:02:29	we are in the frequency domain
0:02:31	we separate the mixture in each
0:02:33	of the frequency band
0:02:35	and at that we have to go back to time domain
0:02:37	so the premise that
0:02:38	usually we take the first signal is the first being as a first note is second be
0:02:42	and your which is a problem
0:02:43	if the order is different
0:02:46	we you have mixed signal
0:02:47	so meaning that
0:02:48	i'm addition resolution is just actually finding in each of the frequency being
0:02:52	a matrix matrix that we
0:02:54	or me the signal so that we exactly have or with
0:02:58	the right component to go back to time domain
0:03:02	so
0:03:03	there are many review you paper so this is one of them
0:03:06	that present a mini single about the convert source separation uh and also many single about
0:03:11	is a permutation problem so several ms what's of some miss database was or
0:03:16	on
0:03:17	checking the the signal that are separated
0:03:19	and some of the on the futures so that you can be in a station of the future some smooth
0:03:23	spectrum
0:03:24	using so directivity part N
0:03:26	or directly the direction of arrival so
0:03:29	here we are as a interest this five
0:03:31	i would also say that there is also some walk that was considering special i'm guessing
0:03:36	so only walk here for example
0:03:38	some of the work
0:03:39	based especially on the direction of arrival
0:03:41	and this walk
0:03:43	we we
0:03:46	so
0:03:47	here i
0:03:48	give some to on so miss what was a one based on direction estimation rate especially really to this
0:03:56	so
0:03:57	for simple we have a i was sick or a microphone array so the microphone a P P two P
0:04:02	three and we
0:04:03	i defined find some vector was actually for the position of the microphone
0:04:06	and here in a far-field assumption we have a a source that is coming from far
0:04:11	and
0:04:12	we have a vector of called here absolute do you way
0:04:14	that is actually
0:04:16	showing the direction from weight can scope
0:04:18	we can have actually a a direct bus more that of the mixture
0:04:22	in that
0:04:23	each of the colour not the mixing matrix is actually
0:04:26	the steering vector or corresponding
0:04:28	to the direction
0:04:29	from we just rolls is coming like here
0:04:31	so we see
0:04:32	the
0:04:33	uh we see a
0:04:36	so this is a microphone vector or as was on this is actually just ring vectors so this scroll on
0:04:40	this on the you one
0:04:42	these one source of a column on the one depending on different
0:04:45	during vector
0:04:46	when we do the separation actually
0:04:48	we recover
0:04:50	the match that when we inverse it we have a and to make
0:04:53	we can have an estimate of these and the problem of permutation
0:04:56	is actually that
0:04:57	if those are steering columns that would be steering column
0:05:00	which are muted meaning that
0:05:02	here for example this
0:05:04	for vector
0:05:05	is not the first one it can be wanting to me
0:05:07	so
0:05:08	here is how the permutation appear on this and the colour of the separated met
0:05:14	so
0:05:15	actually knowing this we can
0:05:17	this so this is a paper
0:05:19	from a
0:05:19	somewhat a
0:05:21	i a key mckay
0:05:22	lacking of sound
0:05:23	it's a
0:05:25	we can see do the
0:05:26	the racial of the element in the colour on
0:05:29	to get
0:05:30	actually is these but so we see that
0:05:32	this we should know because you is
0:05:33	so microphone we know the position
0:05:35	and this is up to G away
0:05:37	actually if we are know in a region as of argument function
0:05:41	to G some meaning that Z is for example in minus spy
0:05:44	i
0:05:45	then
0:05:46	we can we call work Q
0:05:48	from the racial of the and so the constraint that it put on the sense or is also that
0:05:53	actually
0:05:54	he so this is mainly the distance between some sense as and this is absolute do you a
0:05:58	and this is more or less and angle between so
0:06:01	and for the actual do used like used and and go
0:06:04	between this vector
0:06:06	and this one
0:06:07	and depending on this angle for different frequency for them for for low frequency to people are
0:06:12	and
0:06:13	actually we we have a and yeah one we are over
0:06:16	when we have a spacing between the microphone
0:06:19	that is over the blue curve and its independent of the angle between those two
0:06:23	if we have a linear rates very easy
0:06:26	but for a cherry or a have for the first check or or or or even a
0:06:29	different form
0:06:30	is not so easy to know which pair we have
0:06:33	some ideas in because we don't know usually Q
0:06:35	so meaning
0:06:36	and if the frequency of meant we see that
0:06:38	the sense so has to be really close
0:06:41	same
0:06:41	for some fixed
0:06:43	send so this stance so for fixed microphones some distance between the sense or
0:06:47	we can actually
0:06:48	we have also limits still up to the blue curve for twenty sent to meet that will you have
0:06:52	and the in so for frequency or or
0:06:55	some value and depending on the angle
0:06:57	so the thing here is that
0:06:59	when we have a
0:07:00	a linear rate
0:07:01	and we can just the
0:07:04	smaller a pair
0:07:05	these these are
0:07:07	these are constant
0:07:08	but but we have we may have an array a to send you to always
0:07:12	but for a a or real rate maybe we want
0:07:14	we may have a
0:07:15	using this power can use this all the per
0:07:18	this one this one they have very different
0:07:20	distance
0:07:24	you there is no using a a good solution that was proposed is actually to start
0:07:28	or is a value for the column
0:07:30	and to stack all the position or a to make a a big uh matrix
0:07:34	and we we get this kind of equations where i will
0:07:38	the
0:07:39	direction of a right but we want to find should do the solution and
0:07:42	we can have at least squares solution so this is still
0:07:44	so walk with somewhat what was a also
0:07:47	oh
0:07:48	and so why do we do that is that
0:07:50	we
0:07:51	estimate
0:07:52	we
0:07:52	blind just suppression some matrices
0:07:55	from there we can get some direction of arrival
0:07:57	and
0:07:58	if we see for the different frequencies the direction of a right so this is
0:08:01	the permutation we see that in this
0:08:04	a C is a for example the first component it's coming from
0:08:07	sometimes so the blue is a first component it maybe coming from this direction
0:08:12	was this direction sometimes actually if we are able to seize direction
0:08:15	and
0:08:16	permit attack to that
0:08:17	we will so the permutation problem
0:08:21	oh
0:08:22	here are in this paper we i interest in the case where they're especially i'm guessing meaning that
0:08:27	this relation
0:08:28	for some frequency else for some sense so pair is not
0:08:32	it's not longer very fine
0:08:33	so meaning that actually
0:08:35	we can introduce a some values so this are in take it actually those in check your
0:08:40	so that we have this relation the
0:08:43	this is not true but this one is true we put some that have a you here so that this
0:08:47	one is two
0:08:47	so to show eight for example for frequency of
0:08:50	two thousand hz and
0:08:52	one sickle a rate
0:08:54	this is actually
0:08:55	so more less the distance between the microphone and the angle between
0:08:59	so a
0:09:01	vector
0:09:02	between the two microphone and the absolute do way
0:09:05	so in red
0:09:06	we have
0:09:07	this
0:09:08	here
0:09:10	okay okay
0:09:10	so we see that it's over
0:09:12	P and minus P and undermine the P
0:09:15	so these are the
0:09:16	but you in take a value
0:09:18	so but you by by to by
0:09:20	that we have to add
0:09:22	the green curve
0:09:23	and this is actually the difference of the two that is always
0:09:27	in the boundary
0:09:28	so this actually
0:09:29	this one the press this one gives this
0:09:33	oh
0:09:34	we can also add this
0:09:35	to the racial of the call on meaning that we have to those term as before but it also a
0:09:40	this
0:09:41	uh
0:09:42	difference is in figure here
0:09:44	so if we stack
0:09:46	the same way those resort
0:09:47	we also get and
0:09:49	equation that should be verified
0:09:51	by a known direction of ball but also
0:09:55	we have those
0:09:56	in a value that appear in the second part C a and here's was value also unknown no
0:10:01	a tree if if there is no single like this
0:10:04	this would be this is it's simple miss we with special and this
0:10:09	so
0:10:10	so here is just to show that uh
0:10:12	we can transform this equation question with a Q and that of that appear we can transform it actually to
0:10:17	would be to a equation that is only we i'd
0:10:19	by this down that
0:10:21	so yeah yeah change of bits and the patients as the first part here i've we name it G G
0:10:26	yeah
0:10:27	it depend actually
0:10:29	of this
0:10:31	but use
0:10:33	which we can see depend
0:10:35	on the
0:10:37	estimated things
0:10:38	from the metrics so it you and of the
0:10:41	colour on so G and of the frequency
0:10:44	this part
0:10:44	C
0:10:45	here
0:10:46	is just
0:10:48	depending of the sense geometry and see every name E
0:10:51	this one i mean
0:10:52	you we see later Y
0:10:53	so we have this equation
0:10:56	oh
0:10:58	the proposed so think is that we would like to solve as a question and
0:11:02	to find actually a what delta
0:11:04	the things that this equation depend we have a a actually the symmetric is not for run so that is
0:11:09	an infinite number of solution
0:11:11	we can
0:11:12	for example simple get a solution with a minimal norm like this
0:11:16	but we have a our interest in an indigo solution to the equation
0:11:20	which is different from this one show
0:11:24	so
0:11:25	i was talking about sparsity also in the introduction because actually
0:11:30	we can know that this that that
0:11:33	G
0:11:33	have a new and trees
0:11:35	for the rows that correspond to
0:11:37	microphone pair without and the other thing for the given frequency
0:11:41	so it means that
0:11:42	if we have a good initial guess but i'm pretty phi can have a initial guess like is this
0:11:47	the difference between this initial guess
0:11:50	and the value "'em" searching should be sparse so
0:11:52	here have for an example
0:11:54	that's say that
0:11:55	i mean rest in
0:11:56	so frequency
0:11:58	two thousand and
0:11:59	one hundred hz and they used to seven hz one for guess
0:12:03	so these are actually here
0:12:05	that that that
0:12:06	in green
0:12:07	so
0:12:08	and they quite similar so if we look as the difference the different is nearly always with zero
0:12:12	except for some value so it's are like to be them the one
0:12:17	well yeah i mean interest in Z is
0:12:19	actually because
0:12:21	we want to tree to like in many at the reason that solve the permutation we get we start from
0:12:26	the lower what frequency where a less permutation and we
0:12:30	or to higher frequency to sort of them so he the same we we
0:12:33	we use the previous
0:12:34	frequency be as a meaning that
0:12:37	for the been G
0:12:39	of for the bin F
0:12:40	at the can and J we use the result we got for the previous B and we start from the
0:12:44	low work
0:12:45	for each case we be so for a what a question so
0:12:48	with the initial guess
0:12:50	here
0:12:51	and this is actually a re the solution so the the real solution of is minimal no
0:12:55	then we take actually is the rounding of distribution to have
0:13:00	to have an intake
0:13:01	and the goal is actually we would like to have this X close
0:13:04	to the indigo so that that were rounding give this it
0:13:08	this is why actually
0:13:10	we were trying to have this initial guess that is close
0:13:14	quite spots
0:13:15	so
0:13:16	this is and
0:13:17	oh first approach S i guess a it's in better solution to find a sparse
0:13:22	direct you sparse solution to this the question but
0:13:25	i i didn't the E D
0:13:27	so
0:13:28	when we have a solution that to we can define the residual which use actually how good the question was
0:13:32	source to this is just actually
0:13:34	the difference between
0:13:36	uh
0:13:37	the solution of the question
0:13:39	and uh well
0:13:41	what is the error
0:13:42	of that
0:13:44	uh a what where steep
0:13:46	so
0:13:47	how do i realise is to permutation resolution
0:13:50	it simply that
0:13:52	when we are
0:13:53	moving from the frequency being F minus one to the frequency F
0:13:58	you there is a permutation say of the column K
0:14:01	and G
0:14:03	so
0:14:04	in the
0:14:05	been F we we use this equation some innings that
0:14:08	we want to solve this equation to find X
0:14:11	here
0:14:11	that is solution of this which question we see that
0:14:14	we are in the row K
0:14:15	so
0:14:16	what the column catch
0:14:18	and so we have here
0:14:20	the K index but because of the permutation here
0:14:23	we will be using
0:14:25	the guess from that correspond to a knows or colour
0:14:28	chip
0:14:29	so
0:14:30	if is two solution
0:14:32	for the current J and K are quite different
0:14:35	we would not find a closing take a solution
0:14:37	meaning that the residual so the error or on the equation
0:14:40	would be large
0:14:42	so
0:14:42	how large
0:14:43	this we depend also of how much uh a noise there is no what estimate meaning
0:14:48	uh if i where bss it's the walk where on not
0:14:51	so
0:14:52	we can of the first way would be to compare as residual to a threshold
0:14:56	decide if that was a permutation on not
0:14:58	but this is not so easy because
0:15:00	of the noise finding this threshold is not is
0:15:03	and as a solution is
0:15:05	we did this for the row K we can do for the road change so we we have another reason
0:15:09	you
0:15:10	or with
0:15:11	and X K and compares the to to decide if there was a permutation on not this will be a
0:15:15	seem you know to was a ms so that compare
0:15:18	uh the direction of a right
0:15:20	the problem is that some
0:15:22	when especially when the absolute
0:15:25	direction of arrival for the colour a quite close
0:15:28	so as to value may be close meetings that actually
0:15:31	even
0:15:32	the the reason you're be small so we we not detect the permutation
0:15:36	just make the read you are in such case
0:15:38	we have actually to compute
0:15:41	here
0:15:42	so absolute you way
0:15:45	we we have to compute that it'd the U A and try to use a
0:15:47	this up to do you a
0:15:49	with the one from the previous frequency to so
0:15:51	this problem
0:15:52	so in this case the mess what got to bit
0:15:54	close a tools or pro
0:15:57	so
0:15:59	when we can see the
0:16:00	uh for so this is the kind of post processing to solve this problem we first consider a all the
0:16:05	frequency bins where a all the row we have small residual
0:16:10	meaning that
0:16:11	we we did that all the frequency be and we can see that or the one for which
0:16:15	we had directly
0:16:17	small residual
0:16:18	for these we estimate
0:16:21	the sum absolute doa is
0:16:23	we have a this absolute you always along the frequency
0:16:27	and for or the are as and
0:16:29	we compare
0:16:30	so
0:16:30	estimated you eight to this average about you and do the clustering according to
0:16:35	so this is very similar ads
0:16:37	a to be to the a approach
0:16:38	where you find some direction of a one and you close to the
0:16:44	so
0:16:45	here i i haven't for that then the lee and you now one D
0:16:48	some simulation results once to make the data
0:16:52	where we can see there are sixteen microphone
0:16:54	uh a a race was sick or microphone so
0:16:56	the drawing that was before
0:16:58	it has a diameter of thirty thirty for one cent to majors
0:17:01	so we can see sixteen Q has something frequency and five hundred to
0:17:05	fifty
0:17:06	so this is how i model that of is estimated colour
0:17:10	so we have
0:17:11	here
0:17:12	oh this would be the problem if they don't not
0:17:14	uh absolute do way
0:17:16	so like these
0:17:17	and i put some error or so
0:17:19	on the angle
0:17:21	that is
0:17:21	that are uniform in gamma
0:17:23	in a
0:17:24	in uh
0:17:26	as they are uniform on the
0:17:29	interval mine got come model so meaning that a some error or on the direction of arrival
0:17:35	and there is also some at know
0:17:37	for
0:17:37	showing the error or the estimation of this one
0:17:41	and
0:17:42	for some of the frequency
0:17:43	so a random permutation of the core of the core and the percentage
0:17:47	they
0:17:48	D of these frequency bins uh
0:17:51	permit it
0:17:52	so how about we measure the performance
0:17:54	is
0:17:55	first
0:17:56	the present age of frequency been with adequate permutation after part
0:18:00	after the processing
0:18:02	and also as ever all
0:18:03	on the absolute there or do you a
0:18:06	estimation
0:18:07	so i that is to experiment vector in the first one we try to see in france
0:18:11	of the different
0:18:12	a parameter
0:18:13	so
0:18:15	the additive noise
0:18:17	the a row and the end goal
0:18:19	and that
0:18:20	is um the racial of for a permit it
0:18:23	uh call
0:18:25	and the second experiment
0:18:26	i'm right and this is done for some fixed the absolute do you a and
0:18:30	we have a rate the resort to a and some uh
0:18:32	a certain number numbers
0:18:33	independent run
0:18:35	the second
0:18:36	experiment
0:18:37	we want to actually
0:18:39	okay so this is Q to actually
0:18:41	we see we want to see the difference between
0:18:43	is the angle between the absolute to you a how it's
0:18:46	it seems finance
0:18:47	on the result because
0:18:50	this is critical especially
0:18:52	"'cause"
0:18:53	this is what create this kind of problem
0:18:59	so this is a result of the first experiment so
0:19:02	first
0:19:04	one case we just compare the residual so meetings that there is no prob
0:19:07	post processing we just compare the with you're we don't compute a
0:19:11	uh
0:19:12	here in this case we don't compute any direction of rival to result
0:19:16	the
0:19:16	to resolve the permutation the second case
0:19:19	we actually do the post processing that much
0:19:21	propose that
0:19:23	we
0:19:23	in this
0:19:24	we make a second pass
0:19:26	to get
0:19:27	the direction of arrival to permit the beans that maybe had a
0:19:30	so
0:19:31	it's a first call and here we see actually
0:19:34	that
0:19:34	this is a in france of that the even noise
0:19:38	okay okay
0:19:39	and
0:19:40	on the permutation ratio and
0:19:42	on the or on the deal so we see act actually
0:19:45	uh
0:19:46	that is an improvement when we do
0:19:48	uh the post processing
0:19:50	for the number of limitation that the result and
0:19:53	and T it's quite constant and you
0:19:56	a set and
0:19:56	i'm not of uh it's quite robust yeah to the
0:19:59	at no
0:20:00	in the second experiment
0:20:02	we we see the in france of the air or on the angle of that you way
0:20:06	so no
0:20:07	how there is this dispersion of that do you S so this would be the case in a room where
0:20:10	there is more rubber break more less reverberation
0:20:14	so
0:20:15	we see that for this one same
0:20:17	and you a and there were all of around the
0:20:20	fifteen degree they is not so much decrease but that does that we see a sharp you decrease meaning that
0:20:25	it's quite sensitive so
0:20:26	this may be a problem
0:20:28	for high reverberant room
0:20:31	in the third colour on we see actually
0:20:33	so different uh
0:20:35	amount of permit date
0:20:36	uh
0:20:37	a column before processing so
0:20:39	how we can friends a result so we see that
0:20:42	with a post processing it's quite clean
0:20:44	well as
0:20:45	it decrease faster are really with no post processing that meaning that
0:20:48	the more corn and we have to that that the less
0:20:50	good we are at
0:20:52	uh something the or where as it's quite a linear so
0:20:56	and same so what so ever and go to increase very fast with the post
0:21:02	oh
0:21:02	the second experiment is actually we have the different of us so this is the angle between
0:21:07	is a two steering vector corresponding to the colour on
0:21:11	and we see how this in france the mess it so the first thing is that in this case
0:21:15	so two curve a very different meanings that
0:21:17	without
0:21:18	the if we just use the residual
0:21:20	so
0:21:21	we don't
0:21:22	we don't try to use
0:21:23	to get is up to you the and self
0:21:25	we need actually to have absolute the you a that that separate separated to to reach
0:21:29	uh
0:21:31	acceptable results
0:21:32	so meaning like
0:21:33	there should be at least thirty forty T we between them whereas
0:21:37	with a post processing
0:21:38	this is not the problem we and Q fifteen degrees here it was to walking
0:21:42	okay
0:21:45	so
0:21:46	to compare that would say that we we consider this problem and the case of special i'm guessing
0:21:51	we we introduce a kind of model for the special at using to solve the permutation so
0:21:55	one thing that has to be done in sector is now my solution to the equation so to find my
0:22:00	sparse solution it's a
0:22:01	uh how to say
0:22:03	a very easy approach that maybe some that to to do
0:22:06	and of course to apply these to real data and compare it with is was of missile
0:22:19	we have time for only
0:22:20	one
0:22:21	question
0:22:29	okay
0:22:30	thank

RESOLVING FD-BSS PERMUTATION FOR ARBITRARY ARRAY IN PRESENCE OF SPATIAL ALIASING

Acoustic Source Separation

Přednášející: Jani Even, Autoři: Jani Even, Norihiro Hagita, ATR, Intelligent Robotics and Communication Laboratories, Japan