PROGRESSIVE DCT BASED IMAGE CODEC USING

STATISTICAL PARAMETERS

Pooneh Bagheri Zadeh, Tom Buggy

School of Engineering and Computing, Glasgow Caledonian University, 70 Cowcaddens Road, Glasgow,UK

Akbar Sheikh Akbari

Department of Electrical and Electronic Engineering, University of Bristol, Woodland Road, Bristol, UK

Keywords: Discrete cosine transform, image compression, perceptual weights, statistical parameters.

Abstract: This paper presents a novel progressive statistical and discrete cosine transform based image-coding

scheme. The proposed coding scheme divides the input image into a number of non-overlapping pixel

blocks. The coefficients in each block are then decorrelated into their spatial frequencies using a discrete

cosine transform. Coefficients with the same spatial frequency at different blocks are put together to

generate a number of matrices, where each matrix contains coefficients of a particular spatial frequency.

The matrix containing DC coefficients is losslessly coded to preserve visually important information.

Matrices, which consist of high frequency coefficients, are coded using a novel statistical encoder

developed in this paper. Perceptual weights are used to regulate the threshold value required in the coding

process of the high frequency matrices. The coded matrices generate a number of bitstreams, which are used

for progressive image transmission. The proposed coding scheme, JPEG and JPEG2000 were applied to a

number of test images. Results show that the proposed coding scheme outperforms JPEG and JPEG2000

subjectively and objectively at low compression ratios. Results also indicate that the decoded images using

the proposed codec have superior subjective quality at high compression ratios compared to that of JPEG,

while offering comparable results to that of JPEG2000.

1 INTRODUCTION

With advances in multimedia technologies, demands

for transmission and storage of voluminous amounts

of multimedia data have dramatically increased. In

recent years wavelet based image coding schemes

have achieved impressive success, mainly due to the

novel approaches taking by these schemes in data

organization and representation of wavelet-

transformed coefficients Ostermann et al. (2004),

Voukelatos and Soraghan (1997), Sheikh Akbari et

al. (2004). Grgic, Grgic and Zovko-Cihlar (2001)

has shown that discrete cosine transform (DCT)

produces slightly better results than wavelets

especially at low compression ratios while its

computational complexity is less expensive than that

of wavelets. A comparative study on wavelets and

DCT reported by Xiong, Ramchandran and Orchard

(1997) shows the main factors to distinguish image

compression schemes are the way the transformed

coefficients are rearranged, quantized and coded

rather than the difference between the transforms

used.

Statistical parameters of the image data have

been used in a number of image compression

techniques and offer promising visual quality

especially at high compression ratios Chang and

Chen (1993), while the application of statistical

parameters of the transformed image data in image

compression is less reported in the literature. Having

knowledge of the statistical behaviour of the DCT

coefficients plays an important role in designing an

efficient compression algorithm. Several studies on

the statistical distribution of the DCT coefficients

have been reported in the literature Eude, Cherifi

and Grisel (1994), Yovanof and Liu (1996) and

Altunbasak and Kamaci (2004). In Yovanof and Liu

(1996) the DCT coefficients were modelled using a

Generalized Gaussian Function. The results showed

that the high frequency and mid frequency DCT

85

Bagheri Zadeh P., Buggy T. and Sheikh Akbari A. (2008).

PROGRESSIVE DCT BASED IMAGE CODEC USING STATISTICAL PARAMETERS.

In Proceedings of the Third International Conference on Computer Vision Theory and Applications, pages 85-92

DOI: 10.5220/0001084800850092

Copyright

c

 SciTePress

coefficients are well approximated by the

Generalized Gaussian Function while the low

frequency and DC coefficient are well approximated

by a mixture of several Generalized Gaussian

Function. In Eude, Cherifi and Grisel (1994), the

DCT coefficients were approximated by a mixture of

Gaussian distribution model and based on this model

a DCT-based compression technique was developed.

This compression algorithm employs a quantization

table that is a modification of the JPEG quantization

table according to their distribution model. Results

indicated superior visual quality in comparison to

that of JPEG.

In this paper, a progressive statistical and DCT

(SDCT) based image-coding scheme is presented.

The proposed coding scheme divides the input

image into a number of non-overlapping blocks and

applies a DCT on coefficients in each block. The

coefficients with the same frequency indices at

different DCT blocks are grouped together and make

a number of matrices. The matrix containing the DC

coefficients is losslessly coded. The matrices

containing high frequency coefficients are coded

using a novel statistical encoder, which is developed

in this paper. The proposed statistical encoder

applies a hierarchical estimation algorithm to code

the coefficients in each matrix. The hierarchical

estimation algorithm assumes that the distributions

of the coefficients in the matrices are Gaussian in

some regions. A threshold on the variance of the

coefficients is used to determine if it is possible to

estimate the coefficients in the input matrix with the

mean value of a single Gaussian distribution or it

needs further dividing into four sub-blocks. This

hierarchal algorithm is repeated until the distribution

of the coefficients in all sub-blocks fulfils the above

criteria. Finally, the mean value of the Gaussian

distribution of each block is taken as an estimation

value for all coefficients in that block. During the

encoding process a quadtree-like binary map is

generated to save a record of the hierarchical

operation, which is used in decoding process. The

rest of the paper is organized as follows: in Section

2 the proposed coding scheme is discussed; Section

3 explains the decoder; experimental results are

presented at Section 4; and finally Section 5

concludes the paper.

2 PROGRESSIVE STATISTICAL

AND DCT BASED IMAGE

ENCODER

A block diagram of the Progressive Statistical

Discrete Cosine Transform (SDCT) based image

encoder is illustrated in Figure 1. A gray scale image

is input to the encoder. The encoder divides the

input image into a number of 8×8 non-overlapping

pixel blocks called B

11

to B

nn

as shown in Figure

1(a). The coefficients in each block are then

transformed into the frequency domain using a DCT

as shown in Figure 1(b) where A

0-ij

to A

63-ij

are DCT

transformed coefficients in the B

ij

block. The

coefficients with the same frequency indices at

different blocks are then grouped together and

generate 64 matrices called M

0

to M

63

, where M

0

contains the DC coefficients and M

1

to M

63

contain

the AC coefficients from the lowest to the highest

frequency respectively. Figure 1(c) shows one of

these matrices (M

k

), where A

k-11

to A

k-nn

in this

matrix represent the coefficients with the same

frequency index (k), which can take a value between

1 and 63, at different transformed blocks. In this

figure, indices 11 to nn represent the position of the

block that the coefficients belong to.

Figure 1(d) illustrates the encoding stage of the

64 matrices. The M

0

, which contains most of the

image energy, is losslessly coded, using lossless

DPCM method. The M

1

to M

63

matrices are coded

individually using the following operations: (i)

Coefficients in each matrix are first level shifted to

have a minimum value (Min) of zero; (ii) the

resulting coefficients are then coded using a novel

statistical encoding algorithm, which is presented in

Sub-section 2.2. The statistical encoder takes

coefficients in each matrix and a threshold value

(generated specifically for that matrix (detailed in

Sub-section 2.1)), and performs the encoding

process. The output of this encoder is a mean vector

(mv), which carries the mean values, and a binary

vector (q), which carries the quadtree-like data. (ii)

Finally a multiplexor puts the encoded information

together and generates a bitstream called BS

L

, where

L specifies the correspondent matrix, as shown in

Figure 1d. The resulting bitstreams are transmitted

from BS

0

to BS

63

sequentially to perform

progressive image transmission.

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

86

Figure 1: Statistical and DCT Based image encoder (a)

non–overlapping blocks in an image (b) DCT transform of

the coefficients in the block ij (c) organization of the

coefficients in matrix M

K

(d) encoding algorithm.

2.1 Threshold Generation

The threshold value for each matrix is generated

using a uniform quality factor and its JPEG

quantization step, which is derived from the JPEG

quantization table and carries perceptual weight for

that frequency band. The threshold values are

calculated using the following empirical formula:

Where Q_step is its related JPEG quantization step,

and the Quality_factor, which takes any positive

values between 0 and 1000, controls the

compression ratio. This empirical formula has been

found to be appropriate for a wide range of test

images, e.g. Lena, House, Elaine, Bee, Goldhill,

peppers, Zelda, Café.

2.2 Statistical Encoder

The block diagram of the new statistical encoder is

shown in Figure 2. The statistical encoder takes the

coefficients of one of the high frequency matrices

(M

1

to M

63

) and a threshold value, generated

specifically for that matrix (detailed in Sub-section

2.1), and performs the encoding process on it. For

simplification, the input matrix in explanation of

the encoder is called U. The encoding process for

the input matrix U is as follows:

The encoder first defines two empty vectors

called mv (mean value vector) and q (quadtree-like

vector). It then calculates the variance (var) and the

mean value (m) of the matrix U and compares the

resulted variance value with the threshold value. If

the variance is less than the threshold value, the

matrix is coded by its mean value (m) and one bit

binary data equal to 0, which are placed in the mv

and q vectors, respectively. Otherwise one bit binary

data equal to one is placed at the q vector and the

size of the matrix is checked. If the size of the

matrix is 2×2, the four coefficients of the matrix are

scanned and placed in the mv vector and encoding

process is finished by sending the mean value vector

mv and the quadtree-like vector q. If the size of the

matrix is greater than 2×2, the matrix U is divided

into four equal non-overlapped blocks. These four

blocks are then processed from left to right, as

shown in Figure 2. For simplification, the

continuation of the coding process of the first block,

U

1

, is discussed. This process is exactly repeated on

the three other blocks.

Processing of the first block U

1

is described as

follows: The variance (var

1

) and the mean value (m

1

)

of the sub-matrix U

1

are first calculated and then the

resulting variance value is compared with the input

threshold value. If it is less than the threshold value,

the calculated mean value (m

1

) is concatenated to the

mean value vector mv and one bit binary data equal

to 0 is appended to the quadtree-like vector q. The

encoding process of this sub-block is terminated at

this stage. Otherwise, the size of the sub-block is

checked. If it is 2×2, one bit binary data equal to 1 is

appended to the current quadtree-like vector q and

the four coefficients of the sub-block are scanned

Threshold = (Q_step

×

Quality_factor)

¼

(1)

(b)

(c)(a)

B

11

B

12

…

B

21

B

22

…

… … …

B

n1

B

n2

…

B

ij

…

B

1n

B

2n

…

B

nn

A

k-11

A

k-12

…

A

k-21

A

k-22

…

… … …

A

k-n1

A

k-n2

…

A

k-ij

…

A

k-1n

A

k-2n

…

A

k-nn

Quality factor

Threshold Generator Q-table

mv

1

M

1

Level shifter

Statistical

encoder

BS

1

MUX1

q

1

Min

1

mv

2

M

2

Level shifter

Statistical

encoder

BS

2

MUX1

q

2

Min

2

mv

63

M

63

Level shifter

Statistical

encoder

BS

63

MUX1

q

63

Min

63

thr

1

thr

2

…thr

63

(d)

M

0

Lossless encoder

BS

0

M

L

BS

L

………………………………

…

B

ij

(b)

D C T T r a n s f o r m

A

0-ij

A

1-ij

A

63-ij

o o o o o o o o o o o o o o o

(b)

(c)(a)

B

11

B

12

…

B

21

B

22

…

… … …

B

n1

B

n2

…

B

ij

…

B

1n

B

2n

…

B

nn

A

k-11

A

k-12

…

A

k-21

A

k-22

…

… … …

A

k-n1

A

k-n2

…

A

k-ij

…

A

k-1n

A

k-2n

…

A

k-nn

(c)(a)

B

11

B

12

…

B

21

B

22

…

… … …

B

n1

B

n2

…

B

ij

…

B

1n

B

2n

…

B

nn

A

k-11

A

k-12

…

A

k-21

A

k-22

…

… … …

A

k-n1

A

k-n2

…

A

k-ij

…

A

k-1n

A

k-2n

…

A

k-nn

B

11

B

12

…

B

21

B

22

…

… … …

B

n1

B

n2

…

B

ij

…

B

1n

B

2n

…

B

nn

B

11

B

12

…

B

21

B

22

…

… … …

B

n1

B

n2

…

B

ij

…

B

ij

…

B

1n

B

2n

…

B

nn

B

1n

B

2n

…

B

nn

A

k-11

A

k-12

…

A

k-21

A

k-22

…

… … …

A

k-n1

A

k-n2

…

A

k-ij

…

A

k-1n

A

k-2n

…

A

k-nn

A

k-11

A

k-12

…

A

k-21

A

k-22

…

… … …

A

k-n1

A

k-n2

…

A

k-ij

…

A

k-ij

…

A

k-1n

A

k-2n

…

A

k-nn

A

k-1n

A

k-2n

…

A

k-nn

Quality factor

Threshold Generator Q-table

mv

1

M

1

Level shifter

Statistical

encoder

BS

1

MUX1

q

1

Min

1

mv

2

M

2

Level shifter

Statistical

encoder

BS

2

MUX1

q

2

Min

2

mv

63

M

63

Level shifter

Statistical

encoder

BS

63

MUX1

q

63

Min

63

thr

1

thr

2

…thr

63

(d)

M

0

Lossless encoder

BS

0

(d)

M

0

Lossless encoder

BS

0

M

L

BS

L

………………………………

…

B

ij

(b)

D C T T r a n s f o r m

A

0-ij

A

1-ij

A

63-ij

o o o o o o o o o o o o o o o

B

ij

(b)

D C T T r a n s f o r m

A

0-ij

A

1-ij

A

63-ij

o o o o o o o o o o o o o o o

PROGRESSIVE DCT BASED IMAGE CODEC USING STATISTICAL PARAMETERS

87

q : = [q , 1] , and divide matrix ‘U’ into four equal non-overlapped blocks

Input Matrix ( U )

mv : = []

q : = []

Calculate

m = mean(U)

var = var(U)

var < thr

Is size = 2x2

Y

mv : = [mv , m]

q : = [q , 0]

mv : = [mv , c1 , c2 , c3 , c4]

q : = [q , 1]

N

Y

U

1

U

4

var

4

< thr

Is size = 2x2

Y

mv

4

: = [mv

3

, m

4

]

q

4

: = [q

3

, 0]

mv

4

: = [mv

3

, c1 , c2 , c3 , c4]

q

4

: = [q

3

, 1]

N

Y

Calculate m

4

= mean (U

4

)

var

4

= var(U

4

)

q

4

= [q

3

, 1]

U

2

U

3

Divide matrix ‘U

1

’ into four equal non-overlapped blocks

var

1

< thr

Is size = 2x2

Y

mv

1

: = [mv , m

1

]

q

1

: = [q , 0]

mv

1

: = [mv , c1 , c2 , c3 , c4]

q

1

: = [q , 1]

N

Y

Calculate m

1

= mean (U

1

)

var

1

= var(U

1

)

q

1

: = [q , 1]

Divide matrix‘U

4

’ into four equal non-overlapped blocks

U

11

U

12

U

13

U

14

U

41

U

42

U

43

U

44

….

…

...

Divide ‘U

n

’, the 4x4 matrix, into four non-overlapped 2x2 blocks

U

n1

var

n1

< thr

Y

mv

n1

: = [mv

n-1

, m

n1

]

q

n1

: = [q

n-1

, 0]

mv

n1

: = [mv

n-1

, c1 , c2 , c3 , c4]

q

n1

= [q

n-1

, 1]

N

Calculate m

n1

= mean (U

n1

)

var

n1

= var(U

n1

)

Divide ‘U

m

’, the 4x4 matrix, into four non-overlapped 2x2 blocks

q

m4

: = [q

m3

, 1]

var

m4

< thr

Y

mv

m4

: =[mv

m3

, m

m4

]

q

m4

: = [q

m3

, 0]

mv

m4

: = [mv

m3

, c1 , c2 , c3 , c4]

N

Calculate m

m1

= mean (U

m1

)

var

m1

= var(U

m1

)

U

m4

U

n2

...

U

n3

U

n4

U

m3

U

m2

U

m1

….

End

N

q : = [q , 1] , and divide matrix ‘U’ into four equal non-overlapped blocks

Input Matrix ( U )

mv : = []

q : = []

Calculate

m = mean(U)

var = var(U)

var < thr

Is size = 2x2

Y

mv : = [mv , m]

q : = [q , 0]

mv : = [mv , c1 , c2 , c3 , c4]

q : = [q , 1]

N

Y

U

1

U

4

var

4

< thr

Is size = 2x2

Y

mv

4

: = [mv

3

, m

4

]

q

4

: = [q

3

, 0]

mv

4

: = [mv

3

, c1 , c2 , c3 , c4]

q

4

: = [q

3

, 1]

N

Y

Calculate m

4

= mean (U

4

)

var

4

= var(U

4

)

q

4

= [q

3

, 1]

U

2

U

3

Divide matrix ‘U

1

’ into four equal non-overlapped blocks

var

1

< thr

Is size = 2x2

Y

mv

1

: = [mv , m

1

]

q

1

: = [q , 0]

mv

1

: = [mv , c1 , c2 , c3 , c4]

q

1

: = [q , 1]

N

Y

Calculate m

1

= mean (U

1

)

var

1

= var(U

1

)

q

1

: = [q , 1]

Divide matrix‘U

4

’ into four equal non-overlapped blocks

U

11

U

12

U

13

U

14

U

41

U

42

U

43

U

44

….

…

...

Divide ‘U

n

’, the 4x4 matrix, into four non-overlapped 2x2 blocks

U

n1

var

n1

< thr

Y

mv

n1

: = [mv

n-1

, m

n1

]

q

n1

: = [q

n-1

, 0]

mv

n1

: = [mv

n-1

, c1 , c2 , c3 , c4]

q

n1

= [q

n-1

, 1]

N

Calculate m

n1

= mean (U

n1

)

var

n1

= var(U

n1

)

Divide ‘U

m

’, the 4x4 matrix, into four non-overlapped 2x2 blocks

q

m4

: = [q

m3

, 1]

var

m4

< thr

Y

mv

m4

: =[mv

m3

, m

m4

]

q

m4

: = [q

m3

, 0]

mv

m4

: = [mv

m3

, c1 , c2 , c3 , c4]

N

Calculate m

m1

= mean (U

m1

)

var

m1

= var(U

m1

)

U

m4

U

n2

...

U

n3

U

n4

U

m3

U

m2

U

m1

….

EndEnd

End

N

Figure 2: Block diagram of statistical encoder.

and concatenated to the mv vector and encoding

process is ended for this sub-block. If its size is

larger than 2×2, one bit binary data equal to 1 is

concatenated to the current quadtree-like vector q

and the sub-block U

1

is then divided into four equal

non-overlapped blocks. These four new sub-blocks

are named successor sub-blocks and are processed

from left to right in the same way that their four

ancestor sub-blocks were encoded. The above

process is continued until whole successor blocks

are encoded. When the encoding process is finished

two vectors mv and q are passed to the output.

3 PROGRESSIVE STATISTICAL

AND DCT BASED IMAGE

DECODER

Figure 3 shows a block diagram of the progressive

statistical and DCT based image decoder. The

decoding process is started when the reception of the

BS

0

, which contain the DC coefficients of all

transformed DCT blocks, is completed. The decoder

then assumes that the information in the remaining

matrices is zero and reconstructs the output image

with the minimum quality using the received data.

The decoding process is continued as follow: (i) it

waits until the receiving data for the next matrix is

completed; (ii) it assumes that data in the remaining

matrices are zero and reconstructs the image using

information in the received matrices; (iii) if the

reception of the information for all matrices is not

completed, it goes back to stage (i). This process is

repeated until user terminates the process or all

bitstreams are received and the image with the

highest possible quality is reconstructed.

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

88

BS

0

mv

1

BS

1

Statistical Decoder

&

level shifter

DMUX 1

q

1

min

1

….

Lossless decoder

IDCT

Reconstructed

Image

….

∑

R0

R1

R63

mv

2

Place the coefficients in

their original location

at different blocks

M

0

Place the coefficients in

their original location

at different blocks

M

1

BS

2

Statistical Decoder

&

level shifter

DMUX 2

min

2

IDCT

R2

q

2

Place the coefficients in

their original location

at different blocks

M

2

BS

63

Statistical Decoder

&

level shifter

DMUX6 3

min

63

IDCT

mv

63

q

63

Place the coefficients in

their original location

at different blocks

M

63

BS

0

mv

1

BS

1

Statistical Decoder

&

level shifter

DMUX 1

q

1

min

1

….

Lossless decoder

IDCT

Reconstructed

Image

….

∑∑

R0

R1

R63

mv

2

Place the coefficients in

their original location

at different blocks

M

0

Place the coefficients in

their original location

at different blocks

M

1

BS

2

Statistical Decoder

&

level shifter

DMUX 2

min

2

IDCT

R2

q

2

Place the coefficients in

their original location

at different blocks

M

2

BS

63

Statistical Decoder

&

level shifter

DMUX6 3

min

63

IDCT

mv

63

q

63

Place the coefficients in

their original location

at different blocks

M

63

Figure 3: Block diagram of the progressive SDCT decoder.

4 EXPERIMENTAL RESULTS

In order to evaluate the performance of the new

statistical and DCT (SDCT) based image-coding

scheme, three Standard 8-bit greyscale images of

resolution 512×512, ‘Lena’ ‘Elaine’ and ‘House’

were coded using JPEG, JPEG2000 and the

proposed codec. The PSNR measurements for the

encoded images using the three techniques at

different compression ratios are shown in Figure 4.

Results indicate that the proposed coding scheme

outperforms JPEG and JPEG2000, objectively at

low compression ratios while offers inferior

performance at higher compression ratios.

Consequently, to illustrate the visual quality

obtained using the three coding scheme, the decoded

‘Lena’, ‘Elaine’ and ‘House’ images at compression

ratio of 5, 15 and 40 are shown in Figure 5, 6 and 7,

respectively. From Figure 5, it can be seen that all

the decoded test images have very high visual

quality at compression ratio of 5, where the decoded

SDCT images have slightly higher visual quality

than the decoded JPEG images and its quality is

almost the same as that of JPEG2000. From Figure

6, which shows the test images at compression ratio

of 15, some blocking artefacts are visible in the

JPEG images, where SDCT images display higher

visual quality to that of JPEG. The visual quality of

the JPEG2000 images is slightly higher than that of

SDCT. From Figure 7, which illustrate the test

images at compression ratio of 40,it is observed that

the JPEG images exhibit severe blocking artefacts,

which limits the application of this codec in coding

images at high compression ratios while the SDCT

images contain moderate blocking artefacts. From

this figure, it is clear that SDCT offers comparable

visual quality to that of JPEG2000.

Therefore, it can be concluded that the SDCT

techniques offers superior visual quality to that of

JPEG at all compression ratios. This superiority does

not come without a price. The computational

complexity of the proposed codec seems to be

higher than that of JPEG but we have not done any

measurements on the computational cost. In the

proposed codec the DCT transformed coefficients

are first distributed among 64 matrices and then each

matrix is coded using the statistical encoder while in

JPEG the transformed coefficients are first quantized

and then entropy coded. It is also concluded that

SDCT image codec gives comparable visual quality

to that of JPEG2000 at compression ratios below 30,

while it offers an acceptable visual quality at higher

compression. The SDCT image codec offers the

following advantages:

(i) Its architecture facilitates parallel

implementation, as the matrices could be coded

independently.

(ii) Its bitstream is efficient for unequal error

protection, which gives higher performance

when transmitting in noisy environments.

5 CONCLUSIONS

In this paper a new progressive statistical and DCT

based image-coding scheme was developed. It

divides the input image into a number of non-

overlapping pixel blocks. The blocks were then

decorrelated using a DCT transform. The

coefficients with the same frequency index from the

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89

transformed blocks were put together and generate a

number of matrices. The matrix contains DC

coefficients was losslessly coded. The remaining

matrices were coded using a novel statistical

encoder. The statistical encoder estimates the input

matrices with the mean value of a number of 2D

Gaussian distribution. Results shown that the

proposed codec outperforms JPEG subjectively at all

compression ratios. The results indicated that the

SDCT offer comparable subjective quality to

JPEG2000 at medium to low compression ratios.

REFERENCES

Ostermann, J., Bormans, J., List, P., Marpe, D.,

Narroschke, M., Pereira, F., Stockhammer, T. & Wedi,

T., 2004, ‘Video coding with H.264/AVC: Tools,

Performance, and Complexity’, IEEE Circuits and

System Magazine, vol.4, pp.7-28.

Voukelatos, S. P. & Soraghan, J. J., 1997, ‘ Very Low Bit

Rate Colour Video Coding Using Adaptive Subband

Vector Quantization with Dynamic Bit Allocation’,

IEEE Transaction on Circuits and System for Video

Technology, vol. 7, no. 2, pp. 424-428.

Sheikh Akbari, A., Bagheri Zadeh, P., Cochrane, E. &

Soraghan, J.J., 2004, ‘Wavelet-based video codec

using Human Visual System Coefficients for 3G

mobiles’, 12th European Signal Processing

Conference (EUSIPCO 2004), Vienna, Austria.

Grgic, S., Grgic, M. & Zovko-Cihlar, B., 2001,

‘Performance Analysis of Image Compression using

Wavelets’, IEEE Transaction On Industrial

Electronic, vol. 48, no. 3, pp. 682 - 695.

Xiong, Z., Ramchandran, K. & Orchard, M., 1997,

‘Space-frequency quantization for wavelet image

coding’, IEEE Transaction on Image Processing,

vol.6, no.5, pp. 677–693.

Chang, R. F. & Chen, W. T., 1993, ‘Image Coding Using

Variable – Rate Side Match Finite - State Vector

Quantization’, IEEE Transaction on Image

Processing, vol. 2, no. 1,pp. 104-108 .

Eude, T., Cherifi, H. & Grisel R., 1994, ‘Statistical

distribution of DCT coefficients and their application

to an adaptive compression algorithm’ IEEE

International Conference TENCON1994, pp. 427-430.

Yovanof, G.S. & Liu, S., 1996, ‘Statistical analysis of the

DCT coefficients and their quantization error’,

Thirtieth Asilomar Conference on Signals, Systems

and Computers, pp. 601-605.

Altunbasak, Y. & Kamaci, N., 2004, ‘An Analysis Of The

DCT Coefficient Distribution with The H.264 Video

Coder’, ICASSP2004, pp.178-180.

(a)

(b)

(c)

(a)

(b)

(c)

Figure 4: Coding performance of the SDCT, JPEG and

JPEG2000 image codecs: (a) Lena, (b) Elaine and (c)

House.

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(a) SDCT (b) JPEG (c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG (c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG (c) JPEG2000

Figure 5: Coding quality performance of (a) SDCT (b) JPEG and (c) JPEG2000 codecs for ‘Lena’, ‘Elaine’ an

d

‘House’ test images at compression ratio of 5.

(a) SDCT

(b) JPEG

(c) JPEG2000

(a) SDCT

(b) JPEG

(c) JPEG2000

Figure 6: Coding quality performance of (a) SDCT (b) JPEG and (c) JPEG2000 codecs for ‘Lena’, ‘Elaine’ an

d

‘House’ test images at compression ratio of 15.

PROGRESSIVE DCT BASED IMAGE CODEC USING STATISTICAL PARAMETERS

91

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

(a) SDCT (b) JPEG

(c) JPEG2000

Figure 7: Coding quality performance of (a) SDCT (b) JPEG and (c) JPEG2000 codecs for ‘Lena’, ‘Elaine’ an

d

‘House’ test images at compression ratio of 40.

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