Speech Transcript - A SPARSITY BASED CRITERION FOR SOLVING THE PERMUTATION AMBIGUITY IN CONVOLUTIVE BLIND SOURCE SEPARATION

0:00:15	yeah
0:00:16	thank you
0:00:17	um
0:00:17	and let's the some audience left for the last talk of today day
0:00:21	and a
0:00:23	the
0:00:24	it is uh a of different to the talks before
0:00:28	um for for getting line of mike talk we can just this is uh
0:00:33	i to the book were that's uh uh i was taught to
0:00:36	given that very short introduction seduction what lights also plays
0:00:39	say it
0:00:40	what's the problem can load it's case may need to permutation and the greedy and how i'm solving in using
0:00:47	as sparsity basically criteria
0:00:49	so um
0:00:51	and the you a case for like some separation is when you have a cocktail party problem
0:00:56	um we have some sources
0:00:59	uh at this point i say we have
0:01:01	speech sources to a people talking
0:01:04	and he would like to get
0:01:06	sing the components of that
0:01:08	uh but a what what you get a some recordings which are just make chance
0:01:13	these send single components
0:01:15	and um
0:01:18	in this case
0:01:19	but i'm
0:01:20	looking here uh uh we have the
0:01:22	better problem off to the
0:01:24	uh mixture of being convolutive one
0:01:27	as we have to of speech we have reflections and so and so on
0:01:30	so uh
0:01:32	the problem becomes more complicated
0:01:34	and the mathematical formulation for this um we have
0:01:38	some source
0:01:39	some extent
0:01:40	and matrix
0:01:41	at least for the instantaneous then use case
0:01:44	i gets of measurements and what we want to do is to
0:01:48	a estimate might matrix uh separating matrix so we get again to
0:01:52	uh i'll in
0:01:53	a signals
0:01:54	uh for this we had like the ica
0:01:57	so nothing you at this point
0:01:59	uh what we have to um
0:02:01	take into account uh we never now the although of the sources and you never know which energy the sauces
0:02:09	have
0:02:10	um
0:02:11	in my work i used to
0:02:13	done not feature a of the natural gradient
0:02:16	uh as i think if you but you know
0:02:18	oh
0:02:19	for speech signals we need
0:02:22	uh
0:02:23	as always we need some
0:02:25	a a probability dispersion
0:02:27	functions for speech what when considering here
0:02:30	we can safely assume uh we have using a class industry
0:02:35	so
0:02:36	as i you said you have
0:02:39	uh not to simply case we have to convolutive mixture we have
0:02:42	a in this case
0:02:44	you you
0:02:45	different delays you have to reflections and so on
0:02:48	so we model this
0:02:49	using uh a convolution
0:02:52	and uh four
0:02:54	we a situations we have some known that to us
0:02:57	two thousand four thousand taps or whatever
0:03:00	um
0:03:02	estimating these filters directly in time domain
0:03:06	is
0:03:06	hot
0:03:07	possibly but very hard
0:03:09	so the you wouldn't way is to go to the
0:03:12	a time-frequency domain using the short fourier transform
0:03:15	and now what we have is
0:03:18	just again uh what implication in each frequency bin
0:03:21	so uh we can just use the
0:03:25	uh up to a to are you shown in each frequency bin independently
0:03:29	which is again
0:03:31	uh
0:03:32	not a problem
0:03:33	but
0:03:34	no
0:03:35	we have
0:03:36	the problem of
0:03:37	uh the different
0:03:39	and rotation patients and and scaling things uh
0:03:42	and the previous example
0:03:44	can do in you think about that in this case we have to correct
0:03:48	um
0:03:49	the scaling
0:03:50	uh there some standard was you have to solve it
0:03:53	uh
0:03:54	the typical the case is the minimum distance
0:03:57	or often principle
0:03:58	uh which we
0:04:00	multiply the
0:04:01	i'm next matrix by yeah
0:04:03	and the with to tight on you down at them and
0:04:06	uh what
0:04:07	this
0:04:08	and that's that we
0:04:10	uh X and and scaling done by the mixing system
0:04:14	you do not know which was
0:04:15	but at least we do not
0:04:16	at new distortion
0:04:17	just point
0:04:19	um
0:04:19	some new method
0:04:21	uh presented
0:04:22	and last time uh a filter shorting filter shaping
0:04:26	but for these masks that you need
0:04:28	well
0:04:28	um
0:04:29	solve the permutation problem first
0:04:32	uh well it's as
0:04:33	uh you can so it didn't each frequency bin independent
0:04:37	so
0:04:39	we were talking about the permutation problem what what is so how can be
0:04:44	uh well
0:04:45	uh
0:04:46	scrap
0:04:47	in this case
0:04:48	we have to
0:04:49	short time
0:04:50	the
0:04:51	some space two spectrograms for time free transform
0:04:54	of two signals
0:04:55	where just
0:04:56	when you exactly know
0:04:58	these spots a swell between the do use two
0:05:01	uh
0:05:02	spectrograms
0:05:04	when you are we start these signals
0:05:06	back
0:05:06	to time domain of course
0:05:08	both signals appear in boston channels
0:05:11	so again you didn't uh
0:05:14	separate and so you have to correct
0:05:17	for use permutation and these can be
0:05:19	uh and every frequency band different
0:05:22	and usually comes quite complicated
0:05:25	uh usually the two main approaches
0:05:29	uh
0:05:30	the
0:05:31	a lot of paper as in and of friends
0:05:34	concentrate on on direct T V two patents and directions of arrival
0:05:38	uh the idea is
0:05:40	when you have to or mixing matrix as
0:05:42	uh we can just
0:05:44	uh
0:05:44	calculate
0:05:45	to directions with a some come from and assume
0:05:49	uh that one direction is one source
0:05:52	this works
0:05:53	good
0:05:54	a strong we have low reverberation
0:05:56	but i reverberation uh you can't
0:05:59	um um
0:06:01	pinpoint point a the sauce to thing the direction in all frequencies together
0:06:05	uh in this case here
0:06:07	i i used the statistics of the separated signals
0:06:11	um one
0:06:12	trivial simple case is uh
0:06:15	you just
0:06:16	look
0:06:17	such a a line in the neighbouring nine in this say
0:06:20	i
0:06:20	they have to look to same
0:06:22	so
0:06:23	they here they are highly correlated
0:06:26	um
0:06:28	yeah this is true
0:06:29	does this
0:06:31	at least for
0:06:32	when when you are looking for a very near bring bent so we have here to a wreck neighbouring bins
0:06:37	and blue and green and yeah okay yeah highly correlated
0:06:41	if you just
0:06:42	go
0:06:43	a few bins away
0:06:45	yeah i i wouldn't say
0:06:47	these been covered
0:06:49	so the correlation method
0:06:50	is not
0:06:51	so to robust
0:06:53	but uh they have been extensions to make it
0:06:56	uh a lot more robust
0:06:58	oh okay so
0:06:59	yeah
0:07:01	at these um
0:07:02	the correlation coefficients uh
0:07:05	take the
0:07:06	um
0:07:07	and then low
0:07:08	calculate the correlation
0:07:09	and decide
0:07:10	the pen what station
0:07:12	depending on all four possible permutations take
0:07:16	and then
0:07:16	and uh using is uh
0:07:18	uh are you can just use a this this way
0:07:21	as a already said this isn't very robust you have
0:07:24	to make it
0:07:25	a because of the
0:07:27	yeah when comparing more distant bins
0:07:29	a
0:07:30	you just got wrong
0:07:32	uh and then
0:07:33	so um
0:07:35	and
0:07:36	you years ago uh uh just been proposed it is the other so think she you as proposed here
0:07:42	but you don't compare
0:07:44	single bins
0:07:45	uh yeah
0:07:46	but how blocks of bins
0:07:48	so that the S luck like this
0:07:50	you compare
0:07:51	it's a first stage you compare one been but another
0:07:53	zero you one
0:07:55	and calculate a couple
0:07:56	correlation can created in and you get
0:07:59	you permutation and take the next to bins and so and so on
0:08:02	so in this case you have neighbouring bands and you can assume okay to
0:08:07	assumption to five related bins
0:08:09	it's met
0:08:10	in the next step
0:08:12	you take
0:08:13	these to correctly calculated bins
0:08:15	take to two and calculate now
0:08:18	uh these four collation so actually what you get
0:08:21	F here for coefficients
0:08:23	and we have to decide
0:08:24	which one to take to you site which can eight uh which permutation do we take
0:08:29	to big as one
0:08:30	to mean
0:08:31	to always one or whatever
0:08:33	four
0:08:34	but not a problem
0:08:35	here you go to already sixteen and the next
0:08:38	yeah we get a sixty four and so on
0:08:41	so it becomes even harder
0:08:43	um
0:08:44	a simple example for this
0:08:46	um
0:08:46	when we just plot
0:08:48	for the the situation but for a frequency
0:08:51	bins
0:08:52	um
0:08:52	the coefficients yeah
0:08:55	um
0:08:56	for all frequency bins so
0:08:58	and the first page you would just take the correlation it C coefficients
0:09:02	directly
0:09:03	uh on the first of their i don't know
0:09:05	uh
0:09:06	and a
0:09:07	uh okay when you look at this
0:09:10	it's
0:09:10	looks like
0:09:11	just go to uh
0:09:12	well
0:09:13	it just one here and here
0:09:15	hardly
0:09:16	so when you going
0:09:17	next up to next steps
0:09:19	so that's say
0:09:20	you compare
0:09:21	the block
0:09:23	five from that to eight hundred to the block a time that to one thousand
0:09:28	we on that or whatever
0:09:29	you compare all the coefficients well which are and a square
0:09:34	so we have a lot of coefficients which are correctly
0:09:37	and a lot of coefficients with or
0:09:38	not can
0:09:39	and and so on in this case here
0:09:42	K
0:09:44	as we work
0:09:44	here are not
0:09:46	but in the next steps you compare these coefficients
0:09:49	a K just me still worked as might a stable
0:09:52	but this case here
0:09:54	if a lot
0:09:55	one computations
0:09:56	which is a lot of
0:09:57	indicators of our limitations which
0:10:00	in a right and
0:10:01	one conditions so
0:10:03	usually the dyadic sorting scheme
0:10:06	is that are but still
0:10:08	phase
0:10:10	but
0:10:10	so and signal
0:10:13	um
0:10:15	no i want to
0:10:16	um
0:10:18	a present if you approach
0:10:20	uh the first
0:10:21	uh observation i i and you can make it
0:10:24	when you're just take
0:10:26	speech signals
0:10:27	speech signals as past
0:10:29	and um
0:10:32	a mixture of two signals which are in a independent
0:10:35	this last
0:10:37	and a
0:10:38	you can extend this
0:10:41	even if the signals are on a signal
0:10:44	as long as the independent
0:10:47	to mixture is less spots
0:10:50	and just is exactly what we have a a permutation problem we have to bound a signals and one to
0:10:55	look which permutation do we have
0:10:57	so the wrong permutation will be
0:11:00	uh
0:11:01	a past
0:11:03	a a you have he an example of this
0:11:06	uh just
0:11:07	to plain speech signal
0:11:09	but nothing
0:11:10	hadn't yeah
0:11:12	and in this case
0:11:13	i just
0:11:14	most to
0:11:16	hi are that's uh uh of of the signal so that
0:11:19	hi up
0:11:19	half of the signal
0:11:21	to the other so we have to mutation
0:11:23	and the lower
0:11:25	level of of the the R T K that sorting scheme
0:11:28	and when we compare these
0:11:29	we have here a lot of
0:11:31	you was or more zeros
0:11:33	and when you look here we have
0:11:36	clearly a signal which is less spots
0:11:39	and uh
0:11:41	this is exactly what we need to uh
0:11:45	from late
0:11:45	the a new criterion
0:11:48	you want to signal to be S sparse as possible
0:11:51	uh the measurement of sparsity um
0:11:54	for this is an hour of uh to take to
0:11:57	some new method of the lp norm
0:11:59	uh
0:12:01	in my case cases a usually it takes something like zero point one
0:12:05	for for P
0:12:06	but it's not that
0:12:08	and part you can vary
0:12:10	um okay so
0:12:12	uh i there is no
0:12:14	S with the correlation coefficient
0:12:17	we take
0:12:18	our signal
0:12:20	calculate
0:12:22	no not the correlation between two signals
0:12:24	but the sparsity of a sum of two signal
0:12:28	and
0:12:29	take again
0:12:30	the four coefficients
0:12:31	every every one against each other
0:12:34	and you get one
0:12:35	um
0:12:37	yeah coefficients
0:12:38	coefficient which can decide which permutation
0:12:41	the point think about this
0:12:42	snow
0:12:43	we don't take the
0:12:45	coefficients in the time-frequency domain but D transform
0:12:49	is
0:12:50	point process
0:12:51	coefficients
0:12:52	to uh
0:12:53	time domain signal
0:12:54	where we can apply
0:12:56	it it you know
0:12:58	uh
0:13:00	using this
0:13:02	even if we take
0:13:04	that's a hundred frequency bins from K to S
0:13:07	still again P that the calm
0:13:09	just one and coefficient
0:13:11	for the whole sorting she
0:13:14	so when we now know do the
0:13:16	the are or thing
0:13:17	so we have again here and
0:13:20	frequency
0:13:20	just one thing the frequency band transform to the time domain
0:13:24	he again one
0:13:25	E applied to you know
0:13:27	is
0:13:28	and here again
0:13:29	and
0:13:29	at this point that is uh
0:13:31	different
0:13:32	no we transform
0:13:34	to frequency bins the time domain
0:13:38	and calculate again one comes and so and so and so
0:13:41	so it's this point you don't know
0:13:43	have to problem of
0:13:44	which coefficients of this
0:13:46	that's a thousands or or whatever
0:13:49	do you do you takes on you uh but you have always just one coefficient
0:13:53	and
0:13:54	due to the
0:13:55	different
0:13:56	criterion
0:13:58	uh a a it's it's much more robust
0:14:01	mostly
0:14:02	um
0:14:04	i have
0:14:05	done some
0:14:06	simulations
0:14:08	um
0:14:09	so first set
0:14:10	uh uh data set this does a for the set up
0:14:12	use
0:14:12	go
0:14:14	T
0:14:15	um
0:14:16	so on so about last they can set from five years ago so
0:14:20	um
0:14:21	we have
0:14:22	a separate
0:14:23	this this state set that uh is
0:14:25	the lot uh somehow
0:14:27	it's a reverberant
0:14:29	recordings some some speech but to relation is
0:14:32	quite whole
0:14:33	you can when you hear of to is that has that you can see yeah it's
0:14:36	government art
0:14:38	derivations like
0:14:39	this this case
0:14:41	the direction of of uh an approach
0:14:43	it's
0:14:44	very good
0:14:45	um
0:14:47	it
0:14:48	it works because of the low vibration
0:14:51	the proposed method it
0:14:53	not as good
0:14:54	almost
0:14:56	but uh when you're local closely Y
0:14:59	is performing
0:15:00	not that good it's because
0:15:02	it's a very low stage where we compare just one thing and frequency bin
0:15:07	i
0:15:07	yeah uh
0:15:08	happened some limitations to and correct
0:15:11	and uh
0:15:12	so
0:15:13	perhaps
0:15:15	uh
0:15:15	should it this to get so that a bit more
0:15:17	if
0:15:19	uh is
0:15:19	assumption of
0:15:21	sparsity and
0:15:22	solves
0:15:23	a a one pass cygnus is of this is correct
0:15:27	and um
0:15:29	but
0:15:29	when you going to a a set which uh a that the cartons that high reverberation
0:15:34	uh
0:15:35	all over you got
0:15:37	less
0:15:38	uh suppression performance
0:15:41	the do approach
0:15:42	is
0:15:43	because it with to set up you don
0:15:46	to have the uh
0:15:48	the signal coming from one direction because
0:15:50	of the reverberation
0:15:52	but
0:15:53	the new approach we all again get almost the performance of the non right algorithm
0:15:58	uh because this case um
0:16:01	you don't
0:16:02	matter which direction to signal comes as long as we
0:16:05	i able to separate it
0:16:07	in every frequency bin
0:16:09	and um um
0:16:11	so it's not always
0:16:13	matching the non by case
0:16:15	but it's
0:16:15	more robust
0:16:16	compared to the
0:16:18	signal it's of the dot pro
0:16:20	so to conclude
0:16:22	um
0:16:23	the converted by source separation
0:16:25	can be soft and the sorry time-frequency domain
0:16:29	a you have to solve the scaling and permutation
0:16:32	and
0:16:33	no we presented a new algorithm based and sparsity
0:16:37	in the time domain
0:16:38	not as user a and a dating time domain
0:16:43	and with tire of variation we have usually better
0:16:46	separation performance and there
0:16:48	direction five
0:17:09	uh
0:17:11	so
0:17:15	yeah let's a hard a set up it's like seven and a half set and for this i used five
0:17:20	seconds
0:17:22	i i saying
0:17:23	if
0:17:24	an a signal uh enough signal to make i C in each frequency band
0:17:28	then there would be enough signal to make you
0:17:31	you know

A SPARSITY BASED CRITERION FOR SOLVING THE PERMUTATION AMBIGUITY IN CONVOLUTIVE BLIND SOURCE SEPARATION

Non-negative Tensor Factorization and Blind Separation

Presented by: Radoslaw Mazur, Author(s): Radoslaw Mazur, Alfred Mertins, University of Luebeck, Germany