um i will play a will explain and the second what a Q as complex as uh this is the work of uh my former student a a sundry high low grade it in two thousand ten then he would have laughed to present uh this work but if we can a father last week and uh i let that count as an Q um so it's code advice the by michael a the yeah not much of it sure go from carnegie mellon university and i was was at carnegie mellon and died recently moved to you cage thirty um so the word is a concern with you C G signals so electrocardiogram signals and uh you as an example of a measure D C G signal from some data base oh you see it's a periodic repetition of um of sort of elements that we to each other but with slight variation and so if you take out one period then and text books it's typically described like this so this is it is an idiot idealistic representation of that period and the cardiologist they divide this into into pieces um with you see here is a T are interval and S T interval and in the middle of the one that contains the peak that's stick Q R S and of a Q or as complex for yeah i repeated it and um the middle part that's the your S complex of purist's interval and that's what we are concern and uh here's sort of a an extract version of it because you it's kind of a which so this is roughly how it looks like uh and it turns out to as you know cardiologist tell us this as the uh most important part of this uh of the signal and it's used to the for a variety of purposes and in in diagnosed so so cardiologist look at this part to determine whether to and you problems with a hard read them or two detect certain D Cs a typical duration of that part it's hundred milliseconds or a tenth of a second and um you know you may imagine many C G signals are recorded and their stored in a database and if you have millions of patients so uh a and and and many many seconds stand this amounts to you to amount of data so that's why people have started to study the problem of compressing these Q R S comp because you one store it but you want to reduce the amount of data that it takes so of course when you start compressing it you introduce an arrow and you don't want T error to be so large that the diagnostics doesn't work in so all goal is is an essence since to what we what we have in doing is present a method to to compress the Q are as complex while maintaining sufficient quality that's and prior work on this problem because it's so it's relevant and that there was some early work by certain more and others from at one and take compressed to Q are as complex by extracting certain feature that they did reduce the dimensionality uh a late later this work was subsumed by by this is uh a line of work which uh which used or her meat functions to to describe these Q S comp in essence taking that part of the uh taking the cure as complex and expanding it as a linear combination of a mute function and the reason why i meet function came into play was not some the mathematical theory that says a limited functions adjust the functions you want to use here it was just because of the similarity in shape it's just the timit function somehow have system looks similar then together as a cue or as complex and that's why people started doing our approach also is continuous this line of work and um meaning we take that you are as complex and we we expanded into a basis of discrete met function and that this is a somewhat different than the prior work and and i weeks i will explain how the first some background whatever you'd function is to understand to meet function we first have to look at the close "'cause" in the army polynomial i mean polynomials is a is a sequence of polynomials there's one for every degree so the first ones are one and Z uh so here you see for degree zero it's one and then four minus one it's two at zero and then you have a two term occur and that because if defines in um H L S degree at it's easy to see that um and uh because it's a two term occurrence that's a theory that says this put enormous all of can no with respect to some weight function if you take out this weight functions so you divided of you get functions that are truly orthogonal without any weight function and these other of meat function and don't you see that the meat functions it's are in essence the polynomial but no you have to store in front of it and you see there's to E to the minus least square and that just usually make sure that these functions tk very quickly as you go to infinity and so are just a few examples of the first three or meet functions and uh and you see that uh that they have a support that this the entire realign but they D K very quickly because of the each of the minus T square and he you see a little bit you know that good argue some similarity to Q R S K that's why people start and so just the orthogonality condition there exactly orthogonal on the real line but because they D K so quickly you can an essence assigned to them an interval of support and say the orthogonal and that interval approximate just because they are very close to zero outside new see there's also does magic factor uh my trigger parameters mar and that's just stretch as allows you to stretch these functions and that maintains the of net so so the previous work used is for me functions to to express these Q as complex as because of hour that before it was because of visual similarity and the other worked as follows you have a cure or as complex so that one has a certain supports so first you stretch their meet functions to have the same support then you pick the first i don't know however many you one fifteen seventeen a meet functions and you project you Q as complex on to them by just computing the scalar product because they also but now so compute D seattle L coefficients and the more of those you have the better you represent present you see that's the idea and then you keep the first so many fifty that's a use stop somewhere because you don't want to a and seen it many and that's what used store and then if you want to reconstruct you take these fifteen coefficients out of your data base and he the reconstruction for and you get an approximation of the original so that was the approach take now there a problem if you want to implement this yeah this stage you have to compute these integrals and in the computer you cannot do that right you have to is tie some so they went on and discrete times that and if you discrete ties an integral you use a credit sure rule and the at it picked the standard one out of a book and that this as the credits so the whole than an essence what you do is you um you sample at you a function at certain point then you multiply by the length of interval or to see that the usually you have the interval of support and i normalized for minus one to one you divided in this case into a touch of seven just randomly in to seven inch of and now you have to pick one sampling location in each of these intervals and what they did naturally actually the chose an actually actually spaced sampling because it just a natural thing to and then an that since this is the computation you perform you have your samples at exactly space point and then you have this mar you multi but this transform matrix and you C these other meat polynomials evaluated at actually distant point and if you want to reconstruct a and you get the code fish and if you want to reconstruct a you uh you have to use the inverse trend that's fine but there were a a a a few problems with the approach the first is this transform is not orthogonal um and typically be like to have orthogonal transforms for for a variety of three signal processing and then for this kind of transform there that that is not really a very efficient al in other words it's a kind of really comes and you have to do it by definition and that can be very expense so so we built on this approach but but uh changed something namely we change the uh the sampling points because this theory of orthogonal polynomial suggests jess explains that if you sample the actress space are not the natural sampling but in fact uh the sampling points are the remote the proper sampling points should be the roots of of of the and i meet me norm and so i in our case seven uh a here again for price of seven you divide them to seven sub intervals you do not want to sample at these is space points but you want to pick the seventh for me polynomial pick its zeros and these are sort of mathematically than natural sampling and that's why be that interested to see whether these are the actual sampling points so the big you can also get better result and so you see this is here you see it not to space and now you have a slightly different version of transform and reconstruction of the transform yeah the sampling points to are not decrease space and all the transform looks like this and these are the in essence the zeros of the of the and t-norm polynomial and the theory of uh are me in most tells us now that this transform some orthogonal so it you want to reconstruct you can do would with the with the trends what's orthogonal and um um and and just the second part is that actually it's non that for these transforms you have fast out so to test uh to to test this approach to the uh uh uh for the icassp paper to time presenting here we took uh we took a right now a relatively small experiment taking twenty nine Q or as complex of from three different uh uh is C G signal an be compared to a be computed the compression ability and we compared to the previous or meet approach and then we through and also the dft and D T just a yeah because these are the more natural candy that's when you can so in essence dct based compression just like an image process a do a dct transform to keep only the first five or six but visions and that that we tried that also and and here the results um and on the x-axis you C how many coefficients we cap and because once your as complex has twenty seven samples and this particular example of a few people all the if you do a transform and then you keep all the twenty seven coefficient you get perfect reconstruction euro error on the Y is the arrow and the fewer coefficients you keep the large as the error match a now you get these are rate of fronts uh sort of these curve and then depending on the area you can choose how many coefficients you key and every line of the different algorithm and and our new one is the red one not the question is what arrow can you tolerate and i and after the icassp paper we started talking to a cardiologist and we had to a cardiologist go a reconstructed signals and then since the result was that ten percent is good and more is not good so in since you wanna cut here and then you see that for ten percent year the red one is a bit better than the previous one so if you if you quantify that it's again about fifteen twenty percent and the compression ratio that achieve as a factor of five so used store you transform and because to store only like five coefficients before you had twenty seven of sec and uh just a visual confirmation that ten percent is reasonable and twenty percent not so the black line is a a is the a your as complex as a obtained uh as in the database and the the red one is the reconstructed one ten percent error uh and a twenty one of the blue one is with twenty percent you see the blue one is already quite different but really the gold standard is not a a picture like this but what are we real a practitioner say so uh after the get but we continued with the larger experiment where one a brief you show the results because twenty nine or as complex as a relatively small sample so we went into the timit database and B now hundred sixty eight leads so hundred sixty at C E chick uh is C G signals and we two coats five fifteen a hundred of these company and then we also compared to the to the wavelet transform because that's also a natural candidate for for compression um and you the results and you see that uh we have here different arrows because we are a established that more than ten percent is not really acceptable you only need really to look at ten percent error and uh you see here the new algorithm which is a a a minor only a minor modification of the of the one from from this icassp paper since the same one this is the previous one dft based dct based and dwt bay and uh you see always two numbers so the first number is the compression racial by what's factor could you compress the data and you see that all and of large scale experiment we get about a factor of five oh that stuff the a the full to reduction of the amount of data and the the previous algorithm actually on that's larger or uh dataset of worse than on that smaller ones of the smaller one was apparently nice for this previous gore for now here the compression ratio is only three point five so that sort of an improvement of uh fifty percent um and it turns out actually that the dft D T and D W dwt T a a compression to also reasonable candy that uh actually some perform better than their meat based one but the or like in the range around for oh here so yes we we better and you what you've seen the parent as this is how many coefficients you need to keep oh you have a a high compression ratio you only need to keep few coefficients efficient if you have a low one you need to keep more or the method seems to to work okay so my conclusion um i i i the method for the compression of cure S complex as using discrete ties to meet function and it's really a could argue only a small sort of incremental step from the prior work which already used continuous or meat function then using the quadrature rule um but what's really interesting here arguably is that that non could distance sampling performs better than a distance a that's kind of nice because the mathematics of these or meet functions suggests these as natural sampling points i i this functions just have those points as an actual sampling that's actually the reason why we studied the problem because we started actually um see approach to signal processing based on orthogonal polynomials and then we were looking for application and this is one of the applications we found but interesting thing is really that non equidistant sampling you can make say or if you another what's if you deploy it this into real but application maybe be would immediately sampled those C C G signals at those points rather than actually distantly as it's of course done right now and a so we need to actually to interpolate to find the value at these uh these other and uh and compared to the previous methods that's and also to compare to reasonable uh candy that's based on wavelets some cosine transform we achieve a a compression improve compression rates of like twenty to forty percent on no about a some obvious future works one can do and some of these things we already uh where we have been doing in the last three like you know better adjusting those to stretch factor because they you can still do some of fine tuning um there's the question of efficient implementations and be also that some results on having a fast a faster out with for this from me try then of course the question is can you use a similar approach to to other to the other segments of these C G or not to Q as complex but but the other and that concludes my talk thank you very much which work yeah how we choose to segment is that um in sense if you look at the support of the Q or as complex so this my depends on the support of related to the support and so what i say did he looked at the uh interval of support of the cure as signal and that narrows down the choices of sigma very much to like a small interval and then in there you just does a little bit of trial and error and uh because typically only need to do that once for a neat and then you can keep the same signal for your entire lead of Q as complex it's which means you you can actually invest computation time to really fine tune it uh you will not and of i oh so no not a terribly sophisticated approach but the let's say works in correct oh exactly yeah oh what in um uh we do but i mean you get those in from the hard be functions or um always always the non-uniform sampling i mean what are do something instants the sampling points if you want um if you um that's a stick you are as complex has twenty seven samples and uh that so in the beginning you would assume then you take the first twenty seven how me polynomials uh meaning from to be put in a meat functions from number zero to number twenty six and the sampling points are the zeros of the twenty seven one okay and that seems like a we at random choice but if you study mathematical books on orthogonal polynomials then they explain to use that if you choose to this is a general thing more for form of is that if you choose if you use this approach to choosing the sampling points the trends some will become orthogonal okay that doesn't necessarily say that it would perform better for compression but it turned out that actually it it but that that's the oh hmmm yeah the yeah we have no no no oh no insight here it's really i think that is something that you can only find out a group course but Q as complex clearly has a particular shape and the question as the basis function that correspond to this but the different forms which can approximate shape better and and uh yeah no no in so there's not nice biological a model of the heart let's say that would explain to you why what function of the natural one so we have absolutely no inside it's some period in fact it was a surprise to us that and many cases to just using the dct was better than the previous method on a meat functions and that maybe the authors didn't try no problem interesting so