0:00:16 oh we can we that then i'm here to a two percent or people title in compression using iteration to and and aligned action call for supper thinking about and the to jack my kids you yeah so that the right my talk to the three parts the first part for of sparse presentations yeah and motivate how they can be used for image compression and some the issues have come up in this scenario and i trust and the second we we present a present or coverage yeah and then and sorry our contributions and the present results the for sparse person yeah well or a signal vector Y are also given a dictionary matrix E which is a complete unique that has more calls than it has row support and or signal dimension yeah and then you also have a yeah so this is a signal vector Y that's the dictionary a matrix T and this vector X is a sparse representation and what it does this a set like so that's a few columns with the channel matrix D and a waste and to construe to construct an approximation of signal vector Y that's a summation is which shown to be and a vector or so the aim is to use as few courses possible this dictionary matrix and obtain nonetheless a good approximation of Y so the way that one can construct this vector X there's quite a few ways where we use in our work score the matching pursuit algorithm yeah networks like so we initialize the residual vector Y and then the first yeah step of iteration we choose yeah call a from the dictionary one that's most correlated to are vector then we set the coefficient to the projection of the rest of that a call and then we check the condition if we have enough of that as to me X it otherwise we remove the contribution of the new atom to give system residual i didn't the back choose another at of another coefficient and so so this is the matching pursuit algorithm used and and then once we have a vector X how do we use it in image compression there's are ways in which is or don't in the literature this is way we do it a which is more the standard we just take yeah but something and each of them use one block a a to be the signal vector Y yeah and this the sparse approximation X so this is sparse vector X which is that combat representation of the signal vector Y this is the approach we use and the decide which is to come up here the first one is which dictionary D we use yeah and then the are are solution here is to use a tell which is a new their structure dictionary yeah i i've the duration to like dictionary so that's the first sign we should seconds issue issues hi we choose the sparsity of the blocks web image the hold the we choose how many atoms we used to represent each one of this block that gonna process for something the new approach just a little rate distortion this criterion to distribute atoms at the image and the method is we should well as we have the spectra X for each block then how do we construct a bit stream from from that and the were just gonna use standard approach just to that used on you know from a decision of the coefficients have an encoding a fixed and code yeah for the so then the next part of my presentation one is going to address this to decide issues the the choice and that the distribution H that's speak an addiction choice yeah so just do want to date the dictionary structure that we propose yeah we drawn here yeah the sparse approximation creation and this is a dictionary D which is vector yeah a fast matrix it has more columns and or signal dimensions yeah so that but it could be that since interesting "'cause" that's what we it's the sparsity of the vector X and that's what we want to one a sparse vector X yeah and then the them of a complete D is you the map and D S yeah that the more computationally expensive it is to find the best you i the represent the signal vector Y well is still the second issue here and at that point is well them more absence we have a then the more expensive it is in terms of coding rate two yeah yeah to to transmit i so that that that the fires of the atoms used that as an issue so for complete mess but is the sparsity but it also also increases the complexity of the decoding system and the coding rate so what we're going to do is we're going to structure the dictionary matrix T meaning that we're going to constrain and the way in which groups of atoms can be selected yeah so this is the the motivation to the high and duration two and a like dictionary that this constraint are are going to a allow was to enjoy to do over complete and the sparsity of the loop uses E less the constraint or without going to penalty in terms of a compact and coding rate but just a game i i i so what iteration to here and right to to illustrate that i just draw the matching pursuit yeah block diagram for of two slides back is the jury matrix D yeah which is constant for of the durations for the standard case now in our case and i three to in case what we do is we make this matrix D a function of the iteration like so no for with that that's what we call it tuition to because the chance of intuition both B and a which is the i have the same number of atoms and then well the i T king iteration iteration scheme yeah it more of a complete right because we have a lot more i i i to choose from but at the same time the complexity heard and select "'em" and that in this block the same because we have a as columns a when we use the would be back here yeah so we have a problem compared under matching pursuit and also a proper coding rate we use fixed then code to encode yeah to in this just the coding rate is was going to be little to of and so this is structuring approach E allows us to enjoy over complete is we control complexity and coding rate i just drawn here yeah the majors is yeah i i a we're structure so this is the iteration to structure right i where are is the matrix D i yeah yeah and the recording train this structure and the training scheme is very simple we use a top-down approach i so we assume we have a large set of training vectors Y and use all strain vectors to train the first layer the one and then once with trained one fixed it and we compute the rest use the output of the first layer so we have the rest used for the try training set that used to train a second there and so that are that to the last so this is yeah not taken i layer of the i T structure at the last flight so that's that here the input that in progress you and they are dress you i know i i'm going to explore geometric we what happens when as you want of two atoms of this way so here are the input was that use of this the class to just use this great out here and then this subspace it like the screen it here is the i was just pose of the screen so as you can see in that there is a reduction of dimensionality between the one that was use uh i mean one and i rest used for i i rest rest of space this well let's dimensionality mention of that must respect and that was for the but i am here the but what the red reduces dimensionality by one for X in progress the problem is that yeah the union of this two rest of sub-spaces none of us that's entire yeah original signal space so this is a of as this means that the next the the i that's one from the next layer it's going to a have to address the entire signal space so this is what to date yeah why of an operation we propose which works like so yeah so no each some house and alignment matrix yeah and this a of takes for example the green at them and all items with the vertical axis and this score three example and it takes i rested know space of this i i also with the horizontal something and does the same thing that the but at the and are rest of space they but of is again going to file oh the for simple thing so able two of sub-spaces coincide and they're right on the or something meaning that i i was of space using this we rotations still yeah i get get and joyce can just dimensional that we have about T in choosing it is rotation a she's is that i i was vertical axis and i was of is with the for pretty so we further change shoes a rotation majors as or are a lot of interest is so that they are also for i rest of sub-spaces to yeah i have principal component that i was alright right in this for some so the first principal component of the red so space is going to follow along this axis a like was the first principal component of of the screen subspace is going to four a a lot of this as and so one for the a yeah so now i'm just going to read are are are are are previous i i seen this modification this an interest but occasions and that's what i have a year so this is my and to a she two and one dictionary and as you can see no i have a well alignment i tricks per at yeah and because i i went information then but atoms of the matrix with the where with this at this matrix here existing a so must also produce dimensionality the change my as i just what i estimator and so this is a are solution to the first sign we should what which was which to charge this is a each way to use because it enjoys over a complete we do so that C yeah in control coding rate now the second is issue well as at the distribution of process the image here we also have a yeah contribution in this paper a a of that the standard approach used to so a are specified the number of atoms the number of those here is yeah yeah this is the sparse approximation of the input signal vector Y at the standard approach is us to apply a and or threshold to this approximation to are so we choose this this was over at times that satisfy some at maximum or that's a standard approach you are the problem is that we have B blocks in the image and we want to choose the sparsity L and each one of this blocks Y and so we we right a a a a a a global optimal yeah sparse functions approach like so so we want to choose a sparse sparse is of all the routes so that they can do a can look at it yeah block representation a is minimize subject to a constraint on the can be but the root of a box oh this is not very good so so we propose yeah yeah an approximate scheme which works like so yeah we first initialize a sparse is as are also said well of one to zero and then choose the block the second step that of course the biggest problem in terms of arrival distortion reduction it so this is a a this here is the distortion but we used an think occurred sparsity a and this is the potential distortion if we add one more at to twelve summation in two so this is the you or the reduction rather in distortion and that this is the called a penalty include i i i and this one i here so this is distortion for yeah gain a distortion reduction distortion of bit and this is the power of the because problems that true and those it turns so we just a a one more at to this choice and well i i its sparsity P and the P scheme for the second step just a block yeah i i didn't and you add to the choice weapon and so one all still the but but just for the image is one so that's that was a second the site issue and now have some to percent yeah yeah for of but that's that the using is as follows yeah we use the product that the set which is is that a set of non homogeneous face images so the right conditions of the poses not controlled in as we take a training set of the a four hundred images i that training and just and that i a test set a hundred images of this or the showing just right so we use this training set to train i i type structure iteration to align dictionary structure yeah and then test use this yeah this test okay so so just examples of for it the so here are we distortion or cells i have a i a first of all this curves are E i was or a one hundred test image so is it's a two thousand but here that the sort right now i this is true in last B i then i have a three curves for i yeah this is this but curve as with lots of size times can the green of about size twelve and twelve and this one for a of size sixteen ten sixteen so as you can see i to of is quite claim yeah is not and all rates even greater than for nice and than at highest rates this is still at of point nine yeah so the just one out that the coding scheme used to encode the sparse vector X is present so was and yeah in in there rate distortion yeah are work at that transform that we use yeah and the are oh of the of the proposed to yeah at the location scheme okay so now i also have some i only to the results slight have a a two images here that i code using the a two thousand yeah and i as you can see because for use and i are better than of that can you also concluding remarks i started by a summarizing a really let's possible since the presentation are and how we can use the yeah in image compression and then in doing so we ran to three decide issues the first one was what transformation we applied to the signal or to the image blocks well what dictionary use there we propose using and new dictionary structure the i that's true yeah and then there was a question of how do we i i atoms across the image yeah and there are proposed new gram with distortion this approach and then in terms of and and the are X just use very standard approaches so there was nothing there yeah yeah but the best results yeah we're we're good i a from a given to of house yes is was only for the cost features yeah i thank you very much tension you have any questions or that that's i i question but do you can put but it exactly a scheme and so i'm how have compared the okay yeah so there's there's a few things that come to play here so the vector X we have to specify in terms of a i in this is and one does coefficients so for that the since we use the fixed month code it's just going to be a a range up to of the number of that and and for the coefficients week while custom assuming the quantizer then we use a huffman code from that by a special property of the gain of the coefficients because many you think can be most likely that the value of the complete and you give the exponent at no is and that's but does that something of multiple red thanks one more question right you um so recorded sessions so we need a microphone a close to encode addiction on yeah right no we we make the assumption that lectures available at the decoder or okay let's think a speaker