| 0:00:13 | um |
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| 0:00:14 | good morning everybody |
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| 0:00:16 | so i'm very pleased |
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| 0:00:17 | and to present jones work |
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| 0:00:20 | with |
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| 0:00:21 | one eight by a data |
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| 0:00:24 | B |
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| 0:00:25 | there |
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| 0:00:26 | and we are over from integer telecom as the previous speaker but we are located in brittany |
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| 0:00:32 | to compute uh telecom about that |
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| 0:00:34 | so um |
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| 0:00:36 | the topic is uh is uh blind source separation |
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| 0:00:40 | but in the under determined that the mind case |
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| 0:00:43 | and something that i want to emphasise from the onset of the presentation |
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| 0:00:47 | is the fact |
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| 0:00:48 | is that as a result |
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| 0:00:50 | uh strongly relies |
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| 0:00:51 | to show you realise |
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| 0:00:53 | on a sparseness smoother |
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| 0:00:54 | that was introduced several years ago |
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| 0:00:57 | i will come back to this as fast as more that i recommended further |
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| 0:01:01 | because uh uh of its are real events in many signal up |
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| 0:01:04 | a processing applications |
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| 0:01:06 | beyond on the presents one |
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| 0:01:09 | so |
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| 0:01:11 | um |
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| 0:01:12 | i i so the problem states as follows |
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| 0:01:15 | we can see that as and an instantaneous mixing case |
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| 0:01:18 | well we have |
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| 0:01:19 | a known number of unknown sources |
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| 0:01:23 | yeah mixed |
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| 0:01:24 | through matrix a |
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| 0:01:26 | uh for the second of shortening the presentation |
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| 0:01:29 | uh i suppose here that to make is that matrix a is known but in the paper the case where |
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| 0:01:35 | the matrix a is a known as discussed |
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| 0:01:38 | and the resulting channels |
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| 0:01:41 | are corrupted by independent and additive white gaussian noise |
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| 0:01:45 | and we have a set of sensors |
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| 0:01:47 | the number of sensors is assumed to be less strictly less that the number of sources |
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| 0:01:52 | yeah for the estimation |
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| 0:01:54 | of the sources on the basis of the observations |
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| 0:01:57 | is an ill posed problem that detector by considering my assuming that the sources have sparse time-frequency representation |
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| 0:02:05 | and that's in continuation of several papers |
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| 0:02:08 | that are given here |
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| 0:02:10 | so |
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| 0:02:11 | the sparse |
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| 0:02:12 | and |
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| 0:02:13 | uh to the sparseness smooth |
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| 0:02:15 | so uh consider a spectrogram |
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| 0:02:17 | oh well i'm sure |
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| 0:02:19 | in the mixture |
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| 0:02:20 | and you notice that many questions |
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| 0:02:22 | are small |
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| 0:02:23 | and in presence of noise |
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| 0:02:25 | um |
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| 0:02:26 | the the these small uh uh signal components are done by noise |
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| 0:02:31 | and only only a remain visible or the signal components that are a big enough |
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| 0:02:37 | and uh you can resume namely uh consider that the proportion of these large |
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| 0:02:42 | a signal components uh remains lies than or equal to one half |
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| 0:02:47 | so such remarks |
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| 0:02:48 | have already been made by several floors |
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| 0:02:51 | especially in speech audio coding |
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| 0:02:54 | and so we can formalise |
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| 0:02:56 | uh is is |
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| 0:02:57 | as is remark |
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| 0:02:58 | by uh by uh using results or i mean i put is is |
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| 0:03:03 | a publishing two thousand two |
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| 0:03:05 | uh in the paper dedicated to binary hypothesis testing |
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| 0:03:08 | but here as is i put is is used in this paper |
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| 0:03:12 | uh uh can read as follows for the problem |
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| 0:03:16 | so we assume that's true signal components |
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| 0:03:18 | i is uh present a since in the transform domain |
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| 0:03:21 | here we can see those if we domain in some other peoples well considered the wavelet domain of course |
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| 0:03:26 | and with a and we assume that the probability of presence of a signal component |
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| 0:03:31 | is |
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| 0:03:32 | less than or equal to one hand |
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| 0:03:35 | just like what is this is |
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| 0:03:36 | that's when present |
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| 0:03:38 | the signal components are relatively be |
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| 0:03:40 | in the sense that amplitude |
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| 0:03:42 | remains |
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| 0:03:43 | but but some minimum amplitude role |
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| 0:03:47 | so i just stage i must to make to remember |
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| 0:03:49 | first |
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| 0:03:50 | i T disease |
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| 0:03:52 | can be a regarded as constraints |
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| 0:03:54 | is that actually bound our lack of prior knowledge on the signal or uh signal distribution |
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| 0:04:00 | that's to be important because in this paper but in also |
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| 0:04:03 | in all those are papers based on such a a work |
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| 0:04:06 | uh we |
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| 0:04:07 | we assume that the signal distribution he's pretty uh no |
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| 0:04:12 | um |
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| 0:04:13 | Z is i these we say is as if form two weeks |
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| 0:04:16 | weeks sparse smooth or |
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| 0:04:18 | and as that was suggested by one of my for but P D student |
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| 0:04:22 | and we use this terminology now in order to to and this to to make this distinction between the notion |
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| 0:04:28 | of sparsity used for instance in compressed sensing |
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| 0:04:31 | because in compressed sensing you assume that you are you have a a sequence of coefficients that represents your signal |
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| 0:04:37 | but most of these coefficients are a a small or all the zero and the only if you of these |
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| 0:04:41 | coefficients are actually a non zero or large here we do not restrict our attention to search to choose proportion |
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| 0:04:49 | of a signal components |
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| 0:04:50 | is that are small |
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| 0:04:52 | but we are to the contrary |
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| 0:04:54 | we uh propose a framework |
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| 0:04:56 | where is this proportion of a signal component |
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| 0:04:59 | can be close to one half |
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| 0:05:01 | i know that to stick |
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| 0:05:02 | to as if you six |
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| 0:05:04 | uh a |
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| 0:05:05 | i as uh put uh right before |
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| 0:05:08 | so |
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| 0:05:09 | no i'm going to a a two D tried to several states |
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| 0:05:13 | of a a little them based on this past that smaller |
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| 0:05:16 | before presenting some experiment or results |
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| 0:05:19 | and completing the talk |
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| 0:05:22 | so uh i mean some i put use is concerning to as a as a a as the the the |
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| 0:05:27 | blind source uh a suppression problem so the first start with is is that our mixing matrix they |
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| 0:05:33 | is has has for right |
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| 0:05:36 | the second i put use use is that at any time-frequency point the number also sees of active sources |
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| 0:05:43 | uh is strictly less than the number of since |
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| 0:05:45 | that's a two should i put this is because without this i put is is one step of what or |
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| 0:05:50 | our goal them actually phase and i would be important that |
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| 0:05:54 | um |
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| 0:05:55 | and so case i |
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| 0:05:58 | so is the the pros you we we propose here is an extension of what proposed |
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| 0:06:05 | uh what was proposed by i that a B and also over all although of course |
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| 0:06:09 | in in and two thousand seven so |
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| 0:06:12 | and we begin by computing the short time fourier transform was it mixtures |
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| 0:06:16 | in order to get our a sparse representation |
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| 0:06:19 | all of as the noisy uh chose |
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| 0:06:22 | and then is the key point is we estimate the no standard deviation |
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| 0:06:27 | uh we need this estimate because in the uh it we need these estimates |
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| 0:06:32 | this estimate in the next steps |
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| 0:06:34 | and the he point to the main contribution here is that we make this estimation |
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| 0:06:40 | via a a a a a a completely new algorithm which since it has been published in march two thousand |
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| 0:06:45 | eleven |
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| 0:06:46 | so it's called and C you see |
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| 0:06:49 | and a is said with um |
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| 0:06:51 | uh in this paper has been applied to to was a problem for instance |
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| 0:06:55 | uh this problem was the detection of non that you've communication systems in electronic warfare |
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| 0:07:01 | and this this algorithm relies on this they were to call result the based in two and eight |
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| 0:07:07 | and i don't want to get you bow down into the mathematical details concerning this the rain or a as |
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| 0:07:13 | a a and C is it's said |
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| 0:07:15 | but are just want to outline let's as a main principles on which died was them is based |
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| 0:07:20 | and for this i need this random variable |
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| 0:07:23 | so in this run um by board it's K |
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| 0:07:26 | is a is a short fourier transform of the signal or received at since L number T |
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| 0:07:33 | uh |
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| 0:07:34 | two is as she's sort of as the rule is the noise standard deviation |
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| 0:07:38 | and um is the limit the went as S |
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| 0:07:41 | the following |
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| 0:07:42 | first |
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| 0:07:44 | and don't the weeks sparseness smaller like presented before |
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| 0:07:47 | is this random them by gabor |
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| 0:07:49 | tends |
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| 0:07:50 | i uh with respect to a very specific and quite into case |
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| 0:07:53 | convergence criterion |
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| 0:07:55 | two this quantity |
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| 0:07:57 | when the |
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| 0:07:58 | signal to choose a large not so when the signal to noise ratio is good enough |
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| 0:08:03 | when the number of pairs T F that i used to compute this |
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| 0:08:07 | random variable |
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| 0:08:08 | is large enough that said |
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| 0:08:10 | and when the or sort two is chosen according to the meaning of amplitude tool of the O our signal |
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| 0:08:15 | or |
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| 0:08:16 | and the this she's not really a constraint because our meany us we sort that got |
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| 0:08:20 | satisfies the the required condition |
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| 0:08:23 | just said on result |
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| 0:08:25 | a given by system read |
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| 0:08:26 | is that |
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| 0:08:27 | a my the rule is actually so |
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| 0:08:29 | unique positive real number that satisfies this type of coverage |
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| 0:08:34 | shows the you C |
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| 0:08:36 | a that from as follows |
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| 0:08:37 | this is an asymptotic results so we we uh the N C is she is based on the disk straight |
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| 0:08:43 | district cost |
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| 0:08:44 | uh we intend to to uh we we try to minimize this district cost |
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| 0:08:49 | and the pose is do you read by you is that to minimize is this cost is considered as a |
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| 0:08:55 | the solution of this a question |
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| 0:08:57 | and is that |
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| 0:08:58 | uh uh an estimate of the no standard edition that's |
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| 0:09:01 | that it's for a a for this small presentation of the set was a |
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| 0:09:05 | because of the word |
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| 0:09:06 | i i i i i we run out of the |
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| 0:09:09 | so once we have the no standard deviation we can discount reject |
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| 0:09:14 | the time-frequency points |
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| 0:09:15 | um is that correspond to upset of you to noise a or the hard to but we we all week |
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| 0:09:23 | uh noisy signals |
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| 0:09:24 | and we yeah from this rejection biased on there uh resulting sorting taste |
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| 0:09:29 | is that guarantees |
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| 0:09:30 | uh specified five for some probability |
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| 0:09:35 | then we estimate a short time fourier transform of the sue sees i'd execute points |
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| 0:09:39 | and we begin by identifying these active is the active source |
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| 0:09:43 | and C is performed by means of a star now a noise |
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| 0:09:48 | noise so |
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| 0:09:49 | sis space approach |
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| 0:09:50 | uh so briefly |
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| 0:09:52 | G is a set of that they is uh between one and and but we uh i assume that the |
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| 0:09:59 | cardinality of G |
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| 0:10:00 | is cheap be less and and |
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| 0:10:03 | uh we take |
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| 0:10:04 | in a in the mixing matrix a a the cologne |
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| 0:10:08 | uh we was number |
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| 0:10:10 | ease |
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| 0:10:10 | in J and we form matrix a |
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| 0:10:13 | uh and the X G |
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| 0:10:15 | and uh if |
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| 0:10:17 | J |
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| 0:10:18 | uh is just set it as a a a of the source and X sees that are actually present |
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| 0:10:24 | at a time-frequency point |
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| 0:10:26 | C S is then the projection |
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| 0:10:28 | uh the projection of the observation |
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| 0:10:31 | oh onto the noise uh subspace |
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| 0:10:34 | should be uh should be mean me in unionised |
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| 0:10:37 | so um we we proceed like these two i i don't E five |
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| 0:10:42 | uh as a source is and that's at all |
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| 0:10:45 | so to identification of the two sources |
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| 0:10:47 | we |
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| 0:10:48 | do noise the sources |
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| 0:10:50 | by a on linear a feature where seem my the rule is used |
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| 0:10:53 | to address to the future so as a estimate here is used is a pair from here used here and |
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| 0:10:59 | use you know as way |
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| 0:11:01 | and |
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| 0:11:02 | after we just have to compute the inverse time for you transform |
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| 0:11:06 | to estimate the sources in the time domain |
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| 0:11:09 | okay |
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| 0:11:09 | so you we um compare a if we put in red uh those so here we put in a red |
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| 0:11:16 | the the contributions |
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| 0:11:18 | all this work with respect to uh uh uh i side base it work in two thousand seven |
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| 0:11:24 | and i want to and five size here that in needs work |
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| 0:11:28 | in this work |
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| 0:11:29 | the no standard deviation was |
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| 0:11:30 | i seem to be no |
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| 0:11:32 | so we estimate a |
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| 0:11:33 | and uh is this estimate is very helpful to reject the time-frequency points that are |
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| 0:11:38 | uh |
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| 0:11:39 | use less |
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| 0:11:40 | for uh |
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| 0:11:41 | for uh as source suppression |
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| 0:11:44 | and well i um is the a paper by i side B |
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| 0:11:48 | and uh uh uh a put the proposed and is not where as is the the rejection |
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| 0:11:53 | well as uh are formed by us use sorting test where this resource |
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| 0:11:58 | where a manually |
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| 0:11:59 | uh true |
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| 0:12:00 | i'm period features and for every signal-to-noise to we show uh under consideration all of interest |
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| 0:12:06 | you was we get to read a of all this as we replace all of these all these parameters about |
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| 0:12:11 | only one parameter the for on probability |
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| 0:12:14 | and uh based on the estimate at |
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| 0:12:22 | that is so |
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| 0:12:23 | okay |
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| 0:12:24 | so we use uh this |
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| 0:12:27 | but most of automatic approach based on only one part as a four sample but it do we do not |
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| 0:12:32 | we we we we expect no that for me as well as uh is a the may th that would |
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| 0:12:37 | you know make stored uh in in two thousand seven but we do you expect |
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| 0:12:41 | uh to perform for quite as well |
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| 0:12:44 | um and in fact that's that's to here in between you have to the normalized mean square error will um |
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| 0:12:50 | obtained by using a as a or i with them and you read you ha as the result |
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| 0:12:56 | obtained by using a our uh uh new might go was it so as a results are quite the same |
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| 0:13:01 | but i repeat the you are there is only one parameter each which is a for so um well but |
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| 0:13:05 | but fixed at ten or minus tree |
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| 0:13:08 | and so now we have a as a on uh as a a as a the blue black |
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| 0:13:12 | and this is um is aimed at that it teens to the the the the is the difference between our |
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| 0:13:18 | as a noise estimator or based on that robust estimate |
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| 0:13:21 | yeah we have replaced the and C see by the mad estimate of |
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| 0:13:26 | the my to estimate or is a uh a with this use of the might to meet or you you |
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| 0:13:31 | know that there is a significant loss of that from |
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| 0:13:33 | it that's not surprising fact |
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| 0:13:35 | the mad estimate or is a robust estimator and the sense |
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| 0:13:39 | that |
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| 0:13:39 | well and there are oh only a few i would like |
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| 0:13:43 | in the main goal data a them as a my estimate a can estimate and noise standard deviation |
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| 0:13:48 | but here i'll the how to a a a a two D signals |
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| 0:13:52 | and we have seen in the spectrogram that signals component |
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| 0:13:55 | that a signal components are quite |
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| 0:13:57 | present |
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| 0:13:58 | and self for the map estimate a face in this case |
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| 0:14:02 | to the contrary our as a mid and C V C is design |
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| 0:14:06 | uh uh is based on the there were to go from |
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| 0:14:09 | which is aimed at coping with situation where outliers or signal you know |
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| 0:14:14 | ignores are relate to be present |
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| 0:14:15 | and that's a fact that and C V C uh out to a forms of them mad is the is |
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| 0:14:21 | a tuned estimate or the winter alright system of |
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| 0:14:23 | for the same reason |
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| 0:14:25 | but it is it in fact a proposed is the is like to differ |
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| 0:14:29 | okay |
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| 0:14:29 | no and so now i would like to to |
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| 0:14:31 | so i |
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| 0:14:32 | to uh uh to to to some uh and for more name so i don't know whether it's what |
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| 0:14:38 | that's why |
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| 0:14:41 | oh yeah |
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| 0:14:46 | well |
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| 0:14:49 | uh had |
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| 0:14:51 | should had me |
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| 0:14:53 | uh |
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| 0:14:54 | where yeah |
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| 0:14:58 | a a yes i just on i don't have a a a a a low these the fight |
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| 0:15:01 | oh |
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| 0:15:02 | that's a reason okay |
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| 0:15:03 | i completely people tend to a of the fight |
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| 0:15:06 | i so we i was very uh very happy with it |
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| 0:15:10 | uh yes i and if you uh should yes but it will be difficult for you |
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| 0:15:14 | to find and so i'm there so where was very happy with this |
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| 0:15:17 | but uh |
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| 0:15:18 | uh to but |
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| 0:15:19 | um |
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| 0:15:21 | okay |
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| 0:15:22 | so i i i i S this |
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| 0:15:23 | a for at at if people what i and to see that i can so as it is is a |
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| 0:15:27 | these uh |
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| 0:15:28 | i i can prove provides a is a listening things on my on my laptop uh a later |
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| 0:15:33 | so i i i go to the to the competing out |
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| 0:15:36 | so i have fess i the role of sparseness here |
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| 0:15:39 | uh in the presentation |
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| 0:15:40 | as |
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| 0:15:41 | a true the use of the L C S C |
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| 0:15:44 | uh i i also in for size or the fact that |
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| 0:15:46 | uh by using this past mess more we have only one part to to fix |
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| 0:15:51 | and i also would like to and size of fact that we uh as a as this algorithm doesn't take |
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| 0:15:56 | it into account any prior knowledge on the exact nature of source |
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| 0:15:59 | haven't use the fact that the signals out would you once |
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| 0:16:02 | we just |
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| 0:16:03 | i uh uh uh man |
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| 0:16:05 | is that these this north have a sparse time-frequency representation |
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| 0:16:08 | so this kind of a as and can be used |
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| 0:16:11 | for all the types of signals for them for instance like the are and signals |
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| 0:16:16 | um the a use |
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| 0:16:18 | the C a yes C is some to are in the set voice |
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| 0:16:21 | but see it has a very uh uh we but to a back a very uh a a very important |
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| 0:16:25 | to by |
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| 0:16:26 | the to use a is a computationally |
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| 0:16:29 | a has a very high computational or |
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| 0:16:31 | but can be you dash cost |
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| 0:16:33 | and um |
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| 0:16:34 | uh a you want to go we can that |
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| 0:16:36 | with a uh not a new algorithm voice to meetings to not standard deviation |
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| 0:16:40 | it's the date |
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| 0:16:41 | for a a you motion or or uh on P to treat estimate or and this uh i was an |
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| 0:16:47 | should be published in the coming months because well assume it is a |
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| 0:16:50 | the the revised version a a a a few weeks ago |
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| 0:16:53 | and is the date |
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| 0:16:54 | uh relies on i mean even more complete complete |
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| 0:16:58 | uh them to come back grounds that is that the and C E S C |
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| 0:17:02 | it performs as well as a as |
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| 0:17:04 | is a and C C and the ball or its computational cost is significantly less or is that of it |
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| 0:17:10 | a a and C is so that we are going to use these day |
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| 0:17:14 | so no and would like night |
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| 0:17:16 | to be full automatic and would like to get rid of the for um uh probably that we fix |
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| 0:17:21 | i |
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| 0:17:22 | and this is possible or we have to write this for this |
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| 0:17:25 | uh but one of the most for my is is the fact that the date is it set by construction |
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| 0:17:30 | and now to i a detector but and play a detect all capable of coping with quite a a large |
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| 0:17:35 | proportion of uh signal company |
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| 0:17:38 | so uh we i think that i think it just uh a speaker at but i think it's possible to |
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| 0:17:44 | pair form |
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| 0:17:45 | yeah i by as the date |
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| 0:17:46 | and as a a a is the estimation |
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| 0:17:49 | and the detection at at once |
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| 0:17:51 | at the same |
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| 0:17:53 | no um we have considered as the instantaneous case |
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| 0:17:57 | now we have to deal with a convolutive mixing case |
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| 0:18:00 | which is a bit more realistic |
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| 0:18:03 | uh i record that the are discussed the case where a is known and i the that in the paper |
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| 0:18:08 | but we we tackle a problem where a E |
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| 0:18:11 | and |
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| 0:18:11 | okay is this concludes uh my presentation |
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| 0:18:14 | and i thank you very much for a tension |
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| 0:18:30 | i guess that where uh for mixtures and a a not so extreme it channels and for source sources |
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| 0:18:35 | okay okay but |
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| 0:18:37 | sorry |
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| 0:18:38 | think your imaging |
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