image compression using backpropagation neural

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required. Many techniques have been used for image aata compression. / such as with ... t~rough DPCM and adaptive DPCM and at the end vector quantization.
IMAGE COMPRESSION USING BACKPROPAGATION NEURAL NETWORK DR.~

R M. ATTA,

S. EL FISHAWY, DR.M HADHOUD, PROF . K

H. AWADALLA

FACULTY OF ELECTRONIC ENG., MENOUF, EGYPT. 1. ABSTRACT Image data compression is a topic of increasing importance appears in situations where minimum

interest .

number

of

required. Many techniques have been used for image aata

Its ~s

bits

compression

/

such as with nonlinear t~rough

quanti~ation

and delta modulation, as well as

DPCM and adaptive DPCM and at the end vector quantization .

In this paper a three-layer neural network is used Backpropagation

the predictor of the DPCM.

to

algorithm

is

realize used

adapt the weights·of the network. The obtained results show performance (signal to noise ratio) specially for images

to

a

good

that

have

sharp edges and much details. Recorded imagesand computer simulation is used to verify the proposed technique. 2.Introduction Image compression is the problem of coding image data to reduce the amount of data that must be sent to 'transmit the image from location to another, where it. is reconstructed, over an

one

information

channel

(1).

Image compression is possible because nearby pixels

imag~s

are

often

highly

correlated .

which

allows

~hese

in

local

statistical relationships to be exploited . .Many techniques

reduce

transmission

rates

~y

reducing

the

redundancy or correlation within an image and then transmit this new set df d~ta. Predicti~e compression techniques operate the image pixels by use algorithms which make a currently

scanned

Subtracting the

based

pixel

predicted

reduces a difference, transmitted over the

or

value error

~hannel.

error sequence typically

upon from value

prediction

previously the

actual

which

directly

is

of

scanned

the

pixels.

scanned ~hen

on

value

coded

and

Data compression is achieved since the

has

II - 209

a

much

smaller

variance

than

the

.,

orig~nal

image

seq~ence

and thus require fewer bits

per

sample

in

its coded representation. One algorithm frequently

used

is

l2]

pulse code modulation ADPCM (Fig . 1) predic~ion

filter with

adaptive

the

adaptive

which

coefficients

differential

employs to

make

a

linear

the

pixel

prediction.

e(n,m) l(n,m)

-B---.-.

1 (n-m) Predictor .

f' (n,m)

~(n,m)

~(n,m)

PCM

I

J

·

(n-m)

Predictor

:

..................................................................... ............ .

Transmitter

Receiver

Fig.(!) Differential pulse code modulation system . In adaptive linear prediction, an adaptive capability such that the prediction filter coefficients

change

as

is the

used image

..

statistics change, producing a new filter more closely optimized to . the new set of image statistics . As a result, the error sequence will tend to maintain a low power. An algorithm which

has

linear prediction is the algorithm

provides

a

found

least simple

wide

mean

acceptance

square

LMS

computationally

adapting a set of linear prediction

for

adaptive

algorithm.

efficient

coefficients

to

This

way

of

nonstationary

data, and has been used successfully in several applications such as spectral

estimation

and

noise

cancellation

as

well

as

image

in

image

compression. Neural

networks

are

being

increasingly

used

processing, such as image recognition [3] and image restoration This

mainly

due

/

to

their

high

II - 210

computation

speed

and

[4]. their

' I



adaptability, which stems from learning capability.

In

section

predictoris

3

neural

presented~

network

model

and

its

Then, in section 4, computer

usage

as

a

simulation

and

results will .be given.

3 NEURAL NETWORK MODEL. By using three-layer feedtorward neural network shown in Fig with backpropagation algorithm to adapt the weig~ts of the we

~an

construct a predictor for the ADPCM.

network that has been successfully applied problems

ranging

compr,ession [ 5

from

to

a

wide

variety

image

to

scoring

of

J.

let the input preceded

network,

It is a powerful mapping

application

credit

2

pixels

of

the

·input·

first

P ( n, m-1) ,

P ( n, m-2) ,

P(n+l,m-2), P(n+l,m- 1), and P(n+l,m-2)

layer

be

the

P(h-l,m-1),

P ( n-1 , rn ) ,

to

the

currently

pixel P(n,m). Knowing the desired output of this pixel, we it from the actual output of the last 'output '

layer,

error only across the communication channel. At the error signal is used to reconstruct the

original

nearest

th~n

desired subtract send this

-· receiver,

pixel

adding.it to the output of its predictor and also is used

this

P(n,m)

by

to

adapt

network

(Fig .

the weights of its network.- · In. 2),

it~

simplest form · applying to the

the backpropagation training

three-laye~

~lgorithm

begins by

pr~senting

input pattern vector Xkto the network, sweeping forward through system to generate an output response of The output. Ykis in the form

Yk= I

/'

=

[k=O l wk

the

the error

[6] : (sk)

M where sk

Yk' and computing

N

I

[ j=O l

w. J

xj] ]

an

(i )

II-211 'I



and f

is a sigmoid logistic nonlinearity

1 f ( X)

= 1 + e

Where e is a threshold value . The output l a y e r

is in the

( 2)

- ( x - e)

error

of

each

the

in

element

fo~m :

( 3)

Where dk is the desired output of the network .

X

X X X

X

X X

1 2

3

_:)~ yk

4

5

,.

6

7

Fig . 2

.The next step

3-layer feedforward neural network

involves

sweeping

the

ef feet

of

the

backward through the network to associate .a square-error

errors

derivative

6 with each Adaline . The instantaneous square error derivatives first computed for each output layer. The

procedure

of

are

finding

6

hidden l~yer I involves 1 respectively multiplying each derivative 6(!- ) associated with each

associated

with

a

given

Adaline

in

element in the layer ' immediately downstream from a given Adaline the weight that connects it to the

given

Adaline .

These

weighted

square-error derivatives are then added together producing an term

e (I )

which,

· 1.n

t·urn ,

. l.S

. d mu 1 t.1.p 1 1.E!

by

sgm . ( s ( I ) ) ,

derivative of the g£ven Adaline is sigmoid function at operating point . Thus :

II - 212

its

by

error th e

current





(I )

1

=

0

( 4)

2

Each _n f _these derivatives in essence square output error of the network

tells is

to

output of the associated Adaline element. we use only one element in the output layer,

us

how

changes

sensitive in

the

linear

In the network used

layer

and

only

one

the

here, hidden

therefore we have only one 6.

6

The next step is to use this Adaline

gradients. Consider an during presentation k,

to

obtain

somewhere

in

the the

corresponding network

has a weight vector Wk' an input

and linear output sk= WT k Xk. The

instantaneous

which,

vector

gradient

·for

Xk, this

Adaline'element is

"' 2 (ck)

a vk

=

a

wk

"' 2 a (ck)

=

a

a a a

a a

sk "'

( £:

k

sk

a

sk "' 2 (ck)

a

=

a

)

,,

wk T

(XkWk)

wk

2 xk

sk

2 ok xk

( 5)

And finally updating the weights of each Adaline using the method of steepest descent with the

instantaneous

repe?ted by

ll-:Ll]

gradients. The

process

is

,

'

W = W + k+l k

= Where

n

factor, rate.

~(-V

k

Wk ... 2 i-1 6

ry(W k

)~

Xk

-t·

Wk_l) -

( ~J k -

i!

is the momentum constant, 0