0:00:16 | oh |
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0:00:16 | we can we that then i'm here to a two percent or people title |

0:00:19 | in compression using iteration to and and aligned action |

0:00:22 | call for supper thinking about |

0:00:24 | and the to jack my kids you |

0:00:28 | yeah so that the right my talk to the three parts the first part |

0:00:31 | for of sparse presentations |

0:00:33 | yeah and motivate how they can be used for image compression |

0:00:37 | and some the issues have come up in this scenario |

0:00:39 | and i trust and the second |

0:00:41 | we we present a present or coverage |

0:00:44 | yeah and then |

0:00:45 | and sorry our contributions |

0:00:46 | and the present results |

0:00:47 | the for |

0:00:49 | sparse person |

0:00:51 | yeah well |

0:00:52 | or a signal vector Y |

0:00:54 | are also given a dictionary matrix E |

0:00:56 | which is a complete unique that has more calls than it has |

0:01:00 | row support and or signal dimension |

0:01:03 | yeah |

0:01:04 | and then |

0:01:06 | you also have a |

0:01:10 | yeah |

0:01:10 | so this is a signal vector Y |

0:01:12 | that's the dictionary a matrix T and this vector X |

0:01:15 | is a sparse representation |

0:01:16 | and what it does this |

0:01:18 | a set like so that's a few columns with the channel matrix D |

0:01:21 | and a waste and to construe |

0:01:23 | to construct an approximation of signal vector Y that's a summation is which shown to be and a vector or |

0:01:29 | so the aim is to use as few courses possible this dictionary matrix |

0:01:33 | and obtain nonetheless a good approximation of Y |

0:01:35 | so the way that one can construct this vector X |

0:01:38 | there's quite a few ways where we use in our work score |

0:01:41 | the matching pursuit algorithm |

0:01:43 | yeah networks like so |

0:01:45 | we initialize the residual vector Y |

0:01:47 | and then the first |

0:01:49 | yeah |

0:01:50 | step of iteration |

0:01:51 | we choose |

0:01:52 | yeah call |

0:01:54 | a from the dictionary one that's most correlated to are vector |

0:01:56 | then |

0:01:57 | we set the coefficient |

0:01:59 | to the projection of the rest of that |

0:02:01 | a call and then we check the condition if we have enough of that as to me X it otherwise |

0:02:05 | we remove the contribution of the new atom |

0:02:07 | to give system residual |

0:02:09 | i didn't the back |

0:02:10 | choose another at of another coefficient |

0:02:11 | and so so this is the matching pursuit algorithm used |

0:02:14 | and |

0:02:16 | and then once we have a vector X how do we use it |

0:02:18 | in image compression there's |

0:02:21 | are ways in which is or don't |

0:02:22 | in the literature |

0:02:23 | this is way we do it |

0:02:25 | a which is more the standard we just take |

0:02:27 | yeah |

0:02:29 | but something and each of them use |

0:02:31 | one block |

0:02:32 | a a to be the signal vector Y |

0:02:34 | yeah and this the sparse approximation X so this is sparse vector X which is that |

0:02:38 | combat |

0:02:39 | representation of the signal vector Y |

0:02:41 | this is the approach we use |

0:02:42 | and the decide which is to come up here |

0:02:44 | the first one is |

0:02:47 | which dictionary D we use |

0:02:49 | yeah |

0:02:50 | and then the |

0:02:51 | are are solution here is to use a tell which is a new their structure dictionary |

0:02:55 | yeah i i've the duration to like dictionary |

0:02:58 | so that's the first sign we should seconds issue issues |

0:03:01 | hi we choose the sparsity of the blocks web image the hold the we choose how many atoms |

0:03:05 | we used to represent each one of this block |

0:03:08 | that gonna process for something the new approach |

0:03:10 | just a little |

0:03:11 | rate distortion this criterion |

0:03:13 | to |

0:03:13 | distribute atoms at the image |

0:03:15 | and the method is we should |

0:03:17 | well as we have the spectra X |

0:03:18 | for each block |

0:03:20 | then how do we construct a bit stream from from that |

0:03:23 | and the were just gonna use standard approach just to that used on you know from a decision of the |

0:03:26 | coefficients have an encoding |

0:03:28 | a fixed and code |

0:03:29 | yeah for the |

0:03:31 | so then the next |

0:03:32 | part of my presentation one |

0:03:34 | is going to address this to decide issues |

0:03:37 | the the choice |

0:03:38 | and that the distribution |

0:03:39 | H |

0:03:40 | that's speak an addiction choice |

0:03:42 | yeah so just do want to date |

0:03:44 | the dictionary structure that we propose |

0:03:46 | yeah we drawn here |

0:03:48 | yeah the sparse approximation creation |

0:03:50 | and this is a dictionary D which is vector |

0:03:52 | yeah |

0:03:53 | a fast matrix it has more columns and or signal dimensions |

0:03:57 | yeah |

0:03:58 | so that |

0:03:59 | but it could be that since interesting "'cause" that's what we it's the sparsity of the vector X |

0:04:03 | and that's what we want to one a sparse |

0:04:05 | vector X |

0:04:06 | yeah and then |

0:04:08 | the them of a complete D is |

0:04:12 | you |

0:04:19 | the map and D S |

0:04:21 | yeah that |

0:04:22 | the more computationally expensive it is to find the best |

0:04:25 | you i |

0:04:26 | the represent |

0:04:27 | the signal vector Y well |

0:04:29 | is still |

0:04:30 | the second issue here |

0:04:32 | and at that point is |

0:04:33 | well them more absence we have a |

0:04:35 | then the more expensive it is in terms of coding rate |

0:04:38 | two |

0:04:39 | yeah yeah to to |

0:04:40 | transmit |

0:04:41 | i |

0:04:42 | so that that that the fires of the atoms used that as an issue |

0:04:45 | so for complete mess |

0:04:46 | but is the sparsity but it also |

0:04:48 | also increases the complexity of the decoding system |

0:04:51 | and the coding rate |

0:04:53 | so what we're going to do is we're going to structure |

0:04:55 | the dictionary matrix T meaning that we're going to constrain and the way in which groups of atoms can be |

0:05:00 | selected |

0:05:01 | yeah |

0:05:02 | so this is the the motivation to |

0:05:05 | the high and duration two |

0:05:06 | and a like dictionary that this constraint |

0:05:08 | are are going to a allow was to enjoy |

0:05:10 | to do over complete and the sparsity of the loop |

0:05:13 | uses |

0:05:14 | E |

0:05:15 | less the constraint or without going to |

0:05:17 | penalty in terms of |

0:05:19 | a compact |

0:05:20 | and coding rate |

0:05:22 | but just a game |

0:05:24 | i i i |

0:05:26 | so what iteration to here |

0:05:28 | and |

0:05:28 | right |

0:05:30 | to to illustrate that i just draw |

0:05:32 | the matching pursuit |

0:05:34 | yeah |

0:05:35 | block diagram for of two slides back |

0:05:37 | is the jury matrix D |

0:05:39 | yeah |

0:05:40 | which is constant |

0:05:41 | for of the durations |

0:05:43 | for the standard case |

0:05:44 | now in our case and i three to in case |

0:05:46 | what we do is we make this matrix D a function of the iteration |

0:05:50 | like so |

0:05:51 | no for with |

0:05:53 | that that's what we call it tuition to |

0:05:54 | because the chance of intuition |

0:05:57 | both |

0:05:57 | B |

0:05:58 | and a |

0:05:59 | which is the i have the same number of atoms and |

0:06:03 | then |

0:06:05 | well |

0:06:05 | the i T king |

0:06:07 | iteration iteration scheme |

0:06:08 | yeah it |

0:06:09 | more of a complete right because we have a lot more i |

0:06:12 | i i to choose from |

0:06:14 | but at the same time |

0:06:15 | the complexity |

0:06:17 | heard |

0:06:17 | and select "'em" |

0:06:18 | and that in this block |

0:06:20 | the same because we have a as columns |

0:06:23 | a when we use the would be back here |

0:06:25 | yeah |

0:06:26 | so we have a problem compared under matching pursuit |

0:06:29 | and also a proper coding rate we use |

0:06:31 | fixed |

0:06:32 | then |

0:06:32 | code to encode |

0:06:34 | yeah to in this just the coding rate is was going to be little to of and |

0:06:37 | so this is structuring approach |

0:06:39 | E allows us to enjoy over complete is |

0:06:41 | we control |

0:06:42 | complexity and coding rate |

0:06:48 | i just |

0:06:48 | drawn here |

0:06:50 | yeah |

0:06:52 | the majors is yeah i i a we're structure so this is the iteration to structure right |

0:06:57 | i where are is the matrix D i |

0:07:00 | yeah yeah |

0:07:01 | and the recording train this structure |

0:07:03 | and the training scheme is very simple we use a top-down approach |

0:07:06 | i so we assume we have a large set of |

0:07:08 | training vectors Y and use all strain vectors to train |

0:07:12 | the first layer |

0:07:13 | the one |

0:07:14 | and then once with trained one fixed it and we compute |

0:07:17 | the rest use the output of the first layer so we have the rest used for the try training set |

0:07:20 | that used to train a second there |

0:07:22 | and so that are that to the last |

0:07:27 | so this is |

0:07:29 | yeah |

0:07:30 | not taken i layer |

0:07:32 | of the i T structure at the last flight |

0:07:34 | so that's that here |

0:07:36 | the input that in progress you and they are dress you |

0:07:39 | i know i |

0:07:40 | i'm going to explore geometric we what happens when as |

0:07:43 | you want of two atoms of this way |

0:07:45 | so here are |

0:07:46 | the input was that use of this the class to just use this great out here |

0:07:50 | and then this subspace it like the screen it here |

0:07:54 | is the i was just pose |

0:07:56 | of the screen |

0:07:57 | so as you can see |

0:07:59 | in that there is a reduction of dimensionality |

0:08:01 | between the one that was use uh i mean one |

0:08:03 | and i rest used for i |

0:08:06 | i rest rest of space this |

0:08:08 | well let's dimensionality mention of that must respect |

0:08:10 | and that was for the but i am here the but what the red |

0:08:13 | reduces dimensionality by one |

0:08:15 | for X |

0:08:16 | in progress |

0:08:17 | the problem is that |

0:08:20 | yeah the union of this two |

0:08:22 | rest of sub-spaces |

0:08:24 | none of us that's entire |

0:08:25 | yeah |

0:08:26 | original signal space |

0:08:28 | so this is a of |

0:08:29 | as this means that the next |

0:08:31 | the |

0:08:32 | the i that's one from the next layer |

0:08:33 | it's going to a have to address the entire signal space |

0:08:37 | so this is what to date |

0:08:38 | yeah why of an operation we propose which works like so |

0:08:42 | yeah so no each |

0:08:45 | some |

0:08:45 | house |

0:08:46 | and alignment |

0:08:47 | matrix |

0:08:48 | yeah and this |

0:08:49 | a of takes |

0:08:51 | for example the green at them |

0:08:52 | and all items |

0:08:53 | with the vertical axis |

0:08:55 | and this score three example |

0:08:57 | and it takes |

0:08:58 | i |

0:08:58 | rested know |

0:08:59 | space of this i |

0:09:01 | i also |

0:09:01 | with |

0:09:02 | the horizontal something |

0:09:04 | and does the same thing that the but at the and are rest of space |

0:09:07 | they but of is again going to file |

0:09:09 | oh the for simple thing so able two |

0:09:11 | of sub-spaces coincide |

0:09:13 | and they're right on the |

0:09:14 | or something |

0:09:15 | meaning that i i was of space |

0:09:17 | using this |

0:09:18 | we rotations still |

0:09:20 | yeah |

0:09:21 | i get get and joyce can just dimensional |

0:09:25 | that we have about T in choosing |

0:09:28 | it is |

0:09:28 | rotation a she's is that i |

0:09:30 | i was vertical axis and |

0:09:33 | i was of is with |

0:09:34 | the for pretty so we further change shoes |

0:09:36 | a rotation |

0:09:37 | majors as or are a lot of interest is |

0:09:39 | so that they are also for |

0:09:42 | i rest of sub-spaces |

0:09:44 | to |

0:09:45 | yeah i have |

0:09:46 | principal component |

0:09:48 | that i was alright right |

0:09:50 | in this for some so |

0:09:51 | the first principal component |

0:09:53 | of the red |

0:09:54 | so space is going to follow along this axis |

0:09:56 | a like was the first principal component |

0:09:58 | of of the screen subspace is going to four |

0:10:00 | a a lot of this |

0:10:01 | as |

0:10:01 | and so one for the |

0:10:03 | a |

0:10:05 | yeah |

0:10:06 | so now i'm just going to read |

0:10:08 | are are are are are |

0:10:09 | previous i i seen this modification |

0:10:11 | this an interest |

0:10:12 | but occasions |

0:10:13 | and that's what i have a year |

0:10:15 | so this is my and to a she two and one dictionary |

0:10:18 | and as you can see no i have a |

0:10:20 | well alignment i tricks per at |

0:10:22 | yeah and because |

0:10:24 | i i went information |

0:10:25 | then |

0:10:28 | but atoms |

0:10:29 | of the matrix with the where with this |

0:10:31 | at this matrix here |

0:10:32 | existing a so must also produce dimensionality |

0:10:35 | the change my as i just what i estimator and |

0:10:40 | so this is a are |

0:10:41 | solution to the first sign we should what which was which to charge |

0:10:45 | this is a each way to use because it enjoys over a complete |

0:10:48 | we do so that C yeah in control coding rate |

0:10:54 | now the second is issue |

0:10:56 | well as at the distribution of process |

0:10:58 | the image |

0:10:59 | here we also have a |

0:11:01 | yeah |

0:11:02 | contribution in this paper |

0:11:04 | a a of that the standard approach used to |

0:11:06 | so a are specified the number of atoms the number of those here is |

0:11:10 | yeah yeah |

0:11:12 | this is the sparse approximation |

0:11:14 | of the input signal vector Y |

0:11:16 | at the standard approach is us to apply a |

0:11:19 | and or |

0:11:20 | threshold |

0:11:21 | to this approximation to are so we choose |

0:11:22 | this this was over at times that satisfy some at maximum or |

0:11:26 | that's a standard approach |

0:11:28 | you are the problem is that we have |

0:11:30 | B blocks |

0:11:31 | in the image |

0:11:32 | and we want to choose the sparsity L and |

0:11:34 | each one of this blocks Y and |

0:11:36 | so we we |

0:11:37 | right |

0:11:39 | a a a a a a global optimal |

0:11:41 | yeah sparse functions |

0:11:42 | approach like so |

0:11:43 | so we want to choose a sparse sparse is of all the routes |

0:11:46 | so that they can do |

0:11:47 | a can look at it |

0:11:49 | yeah block representation a |

0:11:51 | is minimize subject to a constraint |

0:11:53 | on the can be but the root of a box |

0:11:56 | oh this is not very good |

0:11:58 | so |

0:11:58 | so we propose |

0:11:59 | yeah yeah an approximate |

0:12:01 | scheme |

0:12:02 | which works like so |

0:12:04 | yeah we first initialize a sparse is as are also said well of one to zero |

0:12:08 | and then choose the block |

0:12:11 | the second step that of course |

0:12:12 | the biggest problem |

0:12:13 | in terms of arrival |

0:12:15 | distortion reduction it |

0:12:17 | so this is |

0:12:18 | a a this here is the distortion |

0:12:20 | but we used an |

0:12:22 | think occurred sparsity a |

0:12:23 | and this is the |

0:12:25 | potential distortion if we add one more at |

0:12:28 | to twelve summation in two |

0:12:30 | so this is the you or the reduction rather in distortion |

0:12:33 | and that this is the |

0:12:34 | called a penalty |

0:12:36 | include |

0:12:37 | i i i and this one i here |

0:12:39 | so this is distortion |

0:12:41 | for |

0:12:42 | yeah |

0:12:43 | gain a distortion reduction distortion of bit |

0:12:45 | and this is the power of |

0:12:47 | the because problems that true |

0:12:49 | and those it turns |

0:12:50 | so we just a a one more at to this choice and |

0:12:53 | well |

0:12:54 | i i its sparsity P and the P |

0:12:56 | scheme for the second step just a block |

0:12:58 | yeah i i didn't and you add to the choice weapon and so one all still |

0:13:03 | the but but just for the image is one |

0:13:06 | so that's |

0:13:08 | that was a second |

0:13:09 | the site issue |

0:13:10 | and now have some to percent |

0:13:12 | yeah yeah for of but that's that the using is as follows |

0:13:15 | yeah we use the product that the set which is is that a set of non homogeneous face images |

0:13:19 | so the right conditions of the poses not controlled |

0:13:23 | in as we take a training set of the |

0:13:25 | a four hundred |

0:13:26 | images |

0:13:27 | i that |

0:13:27 | training and just and that i a test set a hundred images of this or the showing just right |

0:13:32 | so we use this training set to train |

0:13:34 | i i type structure |

0:13:35 | iteration to align dictionary structure |

0:13:38 | yeah and then test |

0:13:40 | use this |

0:13:41 | yeah this test |

0:13:43 | okay |

0:13:43 | so |

0:13:44 | so just examples of for it |

0:13:46 | the |

0:13:51 | so here are we distortion or cells |

0:13:53 | i have a |

0:13:54 | i a first of all this curves |

0:13:56 | are |

0:13:57 | E i was or a one hundred test image |

0:14:00 | so is it's a two thousand but here that the sort |

0:14:03 | right now i |

0:14:04 | this is true in last |

0:14:06 | B |

0:14:07 | i then i have a three |

0:14:08 | curves for i |

0:14:09 | yeah this is |

0:14:11 | this but curve as with lots of size times can |

0:14:13 | the green of about size twelve and twelve |

0:14:16 | and this one |

0:14:16 | for a of size sixteen ten sixteen |

0:14:18 | so as you can see i to of is quite claim |

0:14:21 | yeah |

0:14:22 | is not and all rates |

0:14:25 | even greater than for nice |

0:14:27 | and than at highest rates |

0:14:29 | this is |

0:14:29 | still at of point nine |

0:14:32 | yeah |

0:14:33 | so |

0:14:34 | the just one out |

0:14:35 | that the coding scheme used to encode |

0:14:37 | the sparse vector X is present |

0:14:39 | so was |

0:14:40 | and |

0:14:41 | yeah in in there rate distortion |

0:14:43 | yeah are work at that |

0:14:45 | transform that we use |

0:14:46 | yeah and the are |

0:14:47 | oh of the of the proposed to |

0:14:50 | yeah |

0:14:51 | at the location scheme |

0:14:53 | okay so now i also have some |

0:14:56 | i only to the results |

0:14:58 | slight have a a two images here |

0:15:00 | that i code using the a two thousand |

0:15:02 | yeah |

0:15:03 | and i |

0:15:04 | as you can see |

0:15:05 | because for use and i are better than of that can you |

0:15:10 | also |

0:15:11 | concluding remarks i started by |

0:15:13 | a |

0:15:14 | summarizing a really let's possible since the presentation are and how we can use the |

0:15:18 | yeah in image compression |

0:15:21 | and then |

0:15:22 | in doing so we ran to three decide issues |

0:15:24 | the first one was what transformation |

0:15:26 | we applied to the signal |

0:15:28 | or to the image blocks well |

0:15:30 | what dictionary use |

0:15:31 | there we propose using |

0:15:33 | and new dictionary structure |

0:15:34 | the i that's true |

0:15:36 | yeah and then there was a question of how do we |

0:15:38 | i i atoms across the image |

0:15:40 | yeah |

0:15:41 | and there are proposed new |

0:15:43 | gram with distortion this approach |

0:15:45 | and then |

0:15:46 | in terms of |

0:15:47 | and and the are X just use very standard approaches |

0:15:51 | so there was nothing there |

0:15:52 | yeah yeah but the best results |

0:15:54 | yeah we're we're good |

0:15:55 | i |

0:15:56 | a from a given to of house |

0:15:58 | yes is was only for the cost features |

0:16:00 | yeah |

0:16:01 | i thank you very much tension |

0:16:03 | you have any questions or that that's |

0:16:10 | i i question |

0:16:13 | but |

0:16:21 | do you can put but it exactly a scheme |

0:16:24 | and so i'm how have compared the |

0:16:26 | okay |

0:16:27 | yeah |

0:16:28 | so there's |

0:16:29 | there's a few things that come to play here |

0:16:31 | so the vector X |

0:16:32 | we have to specify in terms of a i in this is |

0:16:35 | and one does coefficients |

0:16:37 | so for that the since we use the fixed month code |

0:16:39 | it's just going to be a a range up to |

0:16:41 | of the number of that |

0:16:43 | and and for the coefficients week while custom assuming the quantizer |

0:16:46 | then we use a huffman code from that |

0:16:51 | by a special property of the gain of the coefficients because many you think can be most likely that the |

0:16:56 | value of the complete and you give the exponent at no is and that's |

0:17:00 | but does that something of multiple red |

0:17:03 | thanks |

0:17:06 | one more question right you |

0:17:10 | um |

0:17:12 | so recorded sessions so we need a microphone |

0:17:18 | a close to encode addiction on yeah right |

0:17:21 | no we we make the assumption that lectures available |

0:17:24 | at the decoder |

0:17:25 | or |

0:17:28 | okay let's think a speaker |