Speech Transcript - IMAGE COMPRESSION USING THE ITERATION-TUNED AND ALIGNED DICTIONARY

0:00:16	oh
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

IMAGE COMPRESSION USING THE ITERATION-TUNED AND ALIGNED DICTIONARY

Image Coding

Presented by: Joaquin Zepeda, Author(s): Joaquin Zepeda, Christine Guillemot, Ewa Kijak, INRIA, France