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

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

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