oh oh oh they yeah so what i'd like to talk about the day is uh an application that uh we've recently um had the chance to apply compressed sensing and i think it's a very exciting application a little a i apply applied this thing to ultrasound sound it's go over the ultrasound sound ultrasonic sensing i think it has a lot of implications for active sensing and wideband the raise and various a as so i'll start by setting up the problem um the general idea is that we have an R a and that the are a configuration is not something that wherein in we we are looking into right now uh but we have a general or a and we have a scene and not would like to do is illuminate the scene and a that scene um and we wanna do that as ultrasound and what would like to get is would like to get the three D reflectivity of the now this is not very easy uh that's why we're trying to use a band of sound um and also what we wanna do is you wanna use a lot of the ideas from compressed sensing now what makes us think that we can do that is that every every object in the scene will reflect the old sound but the older sound doesn't penetrate up the object so and i think behind that the object we cannot see so we will appear zero in or in our representation if the object reflects the older sound it means that there was nothing in front of it to clothing it's so everything in front of the object to zero so if we describe is the same let's say by in in three dimensions and one and two and three the number of points in the discrete a station this scene has at most uh and and two times and one points to generally sparse use it's gonna be even sparse there so that makes us uh be hopeful that a processing will work on that C so and it's try to see if we can model this the this whole system and see what we can do with that and then see if that helps as designed the sensing system and a a how to get some reconstruction from that so we'll start with by looking at the single transmitter and a single receiver um in most of this uh talk the transmitters are gonna be blue dots and the receivers green little triangles uh and then i'm gonna be talking about this it's a simple a a a a single scene point with something to in that uh a um i i'm gonna call seen point and and the scene point can think of them as a a whole scene it's a three D scene uh you can think of it as a whole vector that goes from zero to the total number of points and you can that you just like rise the whole three D volume um and the transmitter from that particular scene point has a certain distance uh here here it's the S and and if you can see that they just realise they're bit small um and the receiver has another then so we can we can look at how long it takes the the path for that particular using the speed of sound we can calculate the the distance from transmitter to receiver and see what's the phase delay given a set than oh also the set frequency and if we have a wide don't also can always uh take the for a transfer of that and look at other propagation delay for um for for that particular point so if we look at all the points every point has a particular propagation a delay and if that the transmitter transmits a set a certain impulse um this possible will go get reflected from a point and and get see that the receiver and therefore we can for every point that has that the reflectivity in the scene uh we can write the propagation which we can then put it you know convert it to a matrix form um for all the points in the scene so in general will have a a which is the for every C where it will be and just realise or too small so for every receiver or the frequency spectrum that it will receive we'll just put them all one on on the bottom of the other and the the a matrix captures the pulses that we transmit in the frequency domain and how the they get uh delayed to propagate for every every single point in that and finds and times and in that big you and then the signal the the signal that we're interested in is that reflectivity at which as we said before it's bar so the signal will be high if that point is or like i if there is something at that point a zero otherwise so overall well we get a we get something very from at right you've seen that before it's now you can see uh so we have received a the does i think matrix which is determined by the pulse is that we put in every transmitter and the pulse say and then a scene which we hope is sparse and we think it's sparse now have said that that's a model of the system what can we do to get do the acquisition what can you do to recover um the signal and and how can we how can work with is um um so we know from compressed sensing that in order to do to do that that matrix S to have something quick here's robert this some they various it is some kind of a right B you you can there some or this um and what we have to control this matrix is the pulses that the transmit from its it's transmitter so it's transmitter we design a pulse that are gonna put and and then transmit that um and there are a cover in it you know there are the the limits set we have some from compressed sensing the a a typical K log and the we and so on uh i'm i'm not gonna go do that uh the point is that we want to make that matrix very dave verse some very kind of our i P like so well what the sell what helped single processing randomisation what we're gonna do is we're gonna take pulses that are around and every transmitter all transmitters will transmit at the same time and every transmitter will transmit around "'em" pulse different pulse for transmitter what that will do is that possible get reflected then get acquired by the receiver again with it in frequency and then in this the sensing matrix what the what this allows us to do is have very low coherence some very a very good results a a very good very good um so probability S S L you can think of it um i in the classical sense you know that the you you can't even sometimes in in very simple systems and you can do matched filtering and because the pulses that sorry "'cause" your and you can separate them um and now there are certain your marks said that like to make oh generally the pulse oh the the more dft coefficients you can choose in that paul so if you think of the pulse and time domain taking the frequency domain you have you dft each answer them more dft coefficients you can to for that false and the better chances of recover you have um um also the more transmitters and receivers you have a bigger matrix and you have a uh a better chance of recovery and what does it mean to have more the if dft frequencies that means that um if if pulses finite length and you know there are certain approximations and there it really means uh the dft F length of approximately the length of the pulse more free is available means a longer part so we we need to use either wider bandwidth or longer pulses um now once we have that and have the matrix well you know it's a compressed sensing system we all know we can use L zero minimization which we really can uh we can use we can relax it the no one minimization or we can use one of those ready out in score sound subspace space personal to all brown storm all the M Ps that exist in the field and we can recover the signal now i said before that pulse length and bandwidth term is the number of degrees of freedom so in general you would think that the longer the pulse the better and this is true because you and the pulse to get shows make that gets reflected then you record it but not always so here's the case or we have a very long house but the transmitter is the same as the receiver so what happens we have a finite this but it time that paul street as the system and comes back we still sending pulses and a receiver which is the same as a transmitter cannot switch modes and receive the ball so this is not this is not good so we need to take into account the fact that there is a distance that were sensing and the pulses can not be longer than the round trip of that this so this is something to think about but we can but and that limits the number of degrees of freedom in the diverse we can introduce in the matrix but of course there is a way out of it which is due intermittent sing so intermittent pulsing so we send the small files randomized it comes we wait we receive it it comes back then would send another poll cells are on the eyes different ball so that that can help us in that particular situation so this is the system a another question is that sometimes we have access to a very small physical array so are are a my have very few elements it might not be sometimes they might be linear um we are not a it for example if the R is in there we're not gonna be able we we have a fundamental but like up and down a big you in we're not gonna be able to to reconstruct that sense but that seen that we want to sense uh in in that direction um even even if it's not uh it's not there linear maybe this as are very close to each other and are not enough um in in in a there's not enough separation to reconstruct things and um a and we don't have enough sensors to be able to have a that to very see so what can we do to achieve D reconstruction well this is a technique that um has been used that lot for example synthetic aperture radar so on we create a virtual a so we move the are a at every point would also received data we keep moving it and rate the virtual or synthetic are a if you want um which is well what we can do here of course in this particular case if the if the sensors are linear are there is always an up and down a but it which i'll get to that in a minute uh but for example if we move the are a vertically uh then there is no such thing the the sensors are one i a what does that mean that means we have are one they one for position one of the are a are two a two for position to of the a and so on we can yet a big matrix uh get the scene and and recovered using standard group now oh just realise more time um i'll get to the simulations uh we actually a simulated that system in uh in uh our lab um the the system system that we chose to simulate is uh this particular sensor or it's a relatively wide band sensor the centre frequencies forty heard um you want to be on the relatively high frequency uh for humans and dogs not be here in general if you're doing that uh the bandwidth is approximately ten to fifteen khz so it is a relatively wide band a uh i i i are and wideband sensor this is the frequency response um and the reconstruction of grin which was the users "'cause" sound when there is only just to do that is that if we have prior information on the scene then we can use something like model based compressed sensing or something like that and modify that reconstruction algorithm to be able to a help in the reconstruction from that scene now these are simulation results from a physical are a we had um five transmitters and three receivers uh this is the scene we created uh and this is distances in meters um and this is of course the square we can slight structure without even thing any noise as you can see least squares it's gone a result the scene there's not enough uh rank in the matrix to even produce anything um if we use them processing in particular well as a said to use goes um uh with three db S with thirty db snr by the way the colours here represent the reflectivity the the intensity of the reflectivity of that particular scene um we can get a pretty decent reconstruction a pretty good construction of the same even with twenty db we get some artifacts but with can still get some good reconstruction up to a almost a meter away from the a um uh here's another example of virtual array this is your it's seen i'm not saying uh you scores are constructions kind of pointless uh you could do it you just a noise um here the is all seen um and the the the are is into positions now you might not is that these are not exactly in there there's slightly of said the middle elements of the array are slightly lower than the than the outermost elements and the reason is that we want to result this fundamental up and down um but so you want the are rate to be not completely flat a result that uh this is the scene and this is what we can recover even with ten db signal-to-noise ratio which is and these are meters uh which is pretty a pretty bad um so in conclusion um i'd like to make some remarks so we didn't do would where i think where the first that i've seen that we have all ultrasonic three D reconstruction using a single or eight um and what we exploit it is the near field properties is and and also and compress size in of course but we also um real exploit the fact that there is wide band uh now i have to make a a a a point in that uh time and note here that uh typically if you look for ultrasonic sensors um there really keen to be narrowband uh i typical ultrasonic applications i what people look for them is very narrow field of view and very in our band then the two are compatible but in general uh this is what people want which is completely opposite to what we want what what is nice is that actually if you wanna make the are a wide band you also why don't the field of view so this is if you want to make the sensor or then a you know you why in the field of view which is really good for us so there are there exist if you sense like the one i so that can have a band uh sense now there are certain uh resolutions versus scene that trade offs um generally the higher the frequency you can take the older sound the better or there is a loose and you can get uh that has to do with a wavelet with a wave length of the sound um unfortunately one you're talking about over the air sensing um i frequency means that you can sense and like to centimetres in front of you not more uh if you go like the five hundred khz or something so that's for the khz is a pretty good uh that we use is a pretty good um uh frequency if you wanna do something and the or they're of uh a few meters up to i don't a five six meters um um there are some trade-offs uh in complexity versus performance so what that means uh the number of um of trans uses we get uh we can get better performance we have a that's or a we have a bigger matrix more randomness this that we can introduce there uh of course that means a bigger cost for the E um a and more hardware complexity what is interesting is that if we increase the receivers only a than sorry the number of receiver is the only thing that um at as in terms of the computational cost the number of transmitters really doesn't affect complexity that much except for creating that initial matrix once you create that matrix a number of transmitters uh um a not in the complex the length of the the system a all you have to do with a with the receivers which is good because in general up to up to a point we can increase transmitter an increase they've very city without hurting or are computational complexity now what uh this is a um preliminary to intermediate kind of work um we are building a real system and are actually conducting experiments that uh as we speak that have been is still very good results uh there is some theoretical analysis that uh we need to do and um that the difficulty in this analysis is that we're not talking about an hour of frequencies were actually talking about wideband arrays and oh there are some three key um properties that we need to yeah split there so with that i'm open to questions are common um since it's is is just an to motion or to sex i mean do you you to do do you really "'em" is assumed it's been don't by a group of pose something uh and how how accurately do you know the position of you move to write so this is something that uh we need to to examine um i i expect to will be a bit sensitive that would like an know the most a pretty well and and it's something that actually it's one of are our interest is not really the car is that some mobile or so this is kind of the next things that one of the next things that we really need to study a sense to V R i thing that um is important even with static is is how sense that we are to discrete a sum of the space of course versus fine uh which is also another question that um fine discretization position increases complex the by a lot and it seems that uh we're pretty robust and uh there are ways even even we should go to big extremes are ways that um we can assess city do of course is could a station and then zoom in the to the points of interest and the fine this with basis to talk wonder to show we use of taking advantage of the structure it was firstly i to use for for reconstruction of right this is one reason we use "'cause" sound a there we can do a a a a very good the model based compressed sensing i in which we can we can look at nearby pixels we can look at the fact that for example this is done that sparsity but you know that um if you have a a an object there's nothing behind it so you can set everything behind of to zero uh you know things like that you can do uh we have a look at that and that in this work but is definitely in all a how was it different from a a system problem that we have looking looking at of the people do which is actually compressive sensing and don't to the real and compressive since is for the wheel the machine and the that you oh you are was much more uh difficult issues with a text to the total did by at least the is the more the result oh because of the two than interactions actions model the in section six plus i have a a and in the target is frequency dependent as well i have seen that work at be happy to say i does not how it is that you would you was wide band the use was to speech and the frequency is and the three position C six is a simple okay well out that would be happy to look at that work and uh i at as we had the seem too much work can white but there is uh before okay you i