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