Abstract

In the framework of the image compression by transform coding, we studied two transformation techniques, respectively, used in the JPEG and JPEG2000 standards: the discrete cosine transform (DCT) and the wavelets transform (WT). We also studied the influence of different coding techniques on the compression rate.We compare the performances of different wavelets. The set of the techniques that we implemented have been applied on different types of images.We verified the compromise that exists between the compression rate and the quality of the reconstructed image.We noted that when we apply the wavelet transform, we succeeded with best results of those found by the use of the DCT.We note also that the quality of reconstruction is better as we increase the order of the filter associated to the Daubechies wavelets.

References

1.
CCITT
, “
Video Codec for Audiovisual Services at 64 kbps
,” Recommendation H-261,
1990
, 351 pp.
2.
ISO/IEC JTC1/SC2/WG10, “
Initial Draft for Adaptive Discrete Cosine TransformTechnique for Still Picture data Compression Standard
,”
International Organization for Standardization
,
02
1991
.
3.
ISO/IEC JTC1 Draft international standard 10918-1, “
Digital Compression and Coding of Continuous-Tone Still Images
,” Part 1: Requirements and guidelines,
11
1991
.
4.
Wallace
,
G. K.
, “
Overview of the JPEG (ISO/CCITT) Still Image Compression Standard
,”
Proceedings, SPIE/SPSE Symposium on Electronic Imaging Science & Technologies
, February, 1990.
5.
Pennebaker
,
W.
, “
JPEG Still Image Data Compression Standard
,”
Van Nostrand Reinhold
,
New York
,
1993
.
6.
Cham
,
W. K.
, “
Development of Integer Cosine Transforms by the Principle of Dyadic Symmetry
,”
IEEE Proceedings-I
, Vol.
136
, No.
4
,
08
1989
, pp.
276
-
282
.
7.
Bhaskran
,
V.
and
Konstantinides
,
K.
, “
Image and Video Compression Standards—Algorithms and Architectures
,”
Hewlett-Packard Laboratories, Kluwer Academic Publishe
,
Boston/Dordrecht/London
,
1996
.
8.
ISO/IEC, ISO/IEC 14495-1, “
Lossless and Near Lossless Compression of Continuous-Tone Still Image: Baseline
,” Information technology,
12
1999
.
9.
ISO/IEC, ISO/IEC 14496-2, “
Coding of Audio-Visual Objects: Pan 2: Visual
,” Information technology,
12
1999
.
10.
ISO/IEC JTC1/SC2/WG1, ISO/IEC FCD 14492, “
Coded Representation of Picture and Audio Information—Lossy/Lossless Coding of Bi-Level Images
,”
Core coding system
 [WG1 N 1359],
07
1999
.
11.
ISO1/IEC JTC/SC29/WG1, ISO/IEC FCD 15444-1, “
Information Technology-JPEG 2000 Image Coding System
,”
Core coding system
 [WG 1 N 1646],
03
2000
.
12.
Santa-Cruz
,
D.
,
Ebrahimi
,
T.
,
Askelöf
,
J.
,
Larsson
,
M.
, and
Cristopoulos
,
C. A.
, “
JPEG 2000 Still Image Coding Versus Other Standards
,”
Proceedings of SPIE, Vol. 4115, Applications of Digital Image Processing XXIII
,
Tesher
Andrew G.
Edition,
12
2000
, pp.
446
-
454
.
13.
Rissanen
,
J.
and
Langdon
,
G.
, “
Arithmetic Coding
,”
IBM J. Res. Dev.
 0018-8646, Vol.
23
, No.
2
,
03
1979
, pp.
35
-
43
.
14.
Huffman
,
D. A.
, “
A Method for the Construction of Minimum Redundancy Codes
,”
Proceedings of the IEEE
, Vol.
40
, No. 9,
09
1952
, pp.
1089
-
1101
.
15.
Skodras
,
A. N.
,
Cristopoulos
,
C. A.
, and
Ebrahimi
,
T.
, “
JPEG2000: The Upcoming Still Image Compression Standard
,”
Proceedings of the 11th Portuguese Conference on Pattern Recognition
,
Porto, Portugal
,
05
2000
, pp.
359
-
366
.
16.
Rabbani
,
M.
and
Joshi
,
R.
, “
An Overview of the JPEG 2000 Still Image Compression Standard
,”
Signal Process. Image Commun.
 0923-5965 https://doi.org/10.1016/S0923-5965(01)00024-8, Vol.
17
, No.
1
,
2002
, pp.
3
-
48
.
17.
Santa-Cruz
,
D.
,
Grosbois
,
R.
, and
Ebrahimi
,
T.
, “
JPEG 2000 Performance Evaluation and Assessment
,”
Signal Process. Image Commun.
 0923-5965 https://doi.org/10.1016/S0923-5965(01)00025-X, Vol.
17
, No.
1
,
2002
, pp.
113
-
130
.
18.
Shannon
,
C.
and
Weaver
,
W.
, “
The Theory of Communication
,”
University of Illinois Press
,
Illinois
,
1949
.
19.
Lempel
,
A.
and
Ziv
,
J.
, “
Compression of Individual Sequences Via Variable-Rate-Coding
,”
IEEE Trans. Inf. Theory
 0018-9448 https://doi.org/10.1109/TIT.1978.1055934, Vol.
IT-24
,
1978
, pp.
530
-
536
.
20.
Netravelli
,
A. M.
and
Limb
,
I. O.
, “
Picture Coding: A Review
,”
Proceedings of the IEEE
, Vol.
68
, No. 3,
03
1980
, pp.
366
-
407
.
21.
Jain
,
A. K.
, “
Image Data Compression: A Review
,”
Proceedings of the IEEE
, Vol.
69
, No. 3,
03
1981
, pp. 349-389.
22.
Kunt
,
M.
, “
Source Coding of X-Ray Pictures
,”
IEEE Trans. Biomed. Eng.
 0018-9294, Vol.
25
,
1978
, pp.
121
-
138
.
23.
Averbuch
,
A.
,
Lazar
,
D.
, and
Israeli
,
M.
, “
Image Compression Using Wavelet Transform and Multiresolution Decomposition
,”
IEEE Trans. Image Process.
 1057-7149 https://doi.org/10.1109/83.481666, Vol.
5
, No.
1
,
01
1996
, pp.
4
-
15
.
24.
Barnes
,
C. F.
,
Rizvi
,
S. A.
, and
Nasrabadi
,
N. M.
, “
Advances in Residual Vector Quantization: A Review
,”
IEEE Trans. Image Process.
 1057-7149 https://doi.org/10.1109/83.480761, Vol.
5
, No.
2
,
02
1996
, pp.
226
-
262
.
25.
ACR/NEMA STANDARDS
, “
Publication for Data Compression Standards
,” NEMA Publication PS-2,
Washington, DC
,
1989
.
26.
Makoto
,
Y.
,
Norman
,
D. K.
, and
Sakae
,
O.
, “
Standardisation of Audiovisual Systems in CCITT
,”
IMAGE'COM 90
,
Bordeaux-France
, November 19–21,
1990
, pp.
42
-
47
. 2cf]27]
Jayanta
,
N.
,
Johnston
,
J.
, and
Safranek
,
R.
, “
Signal Compression Based on Models of Human Perception
,”
Proceedings of the IEEE
, Vol.
81
, No. 10,
10
1993
, pp.
1385
-
1419
.
27.
James
,
W. M.
and
Yong
,
H. K.
, “
Adaptive Entropy-Coded Predictive Vector Quantization of Images
,”
IEEE Trans. Signal Process.
 1053-587X, Vol.
40
, No.
3
,
09
1992
, pp.
633
-
643
.
28.
Ben Jebara
,
S.
and
Jaïdane Saïdane
,
M.
, “
Compression d'images satellitaires par quantification vectorielle: optimisation aux bas débits
,”
Journées Tunisiennes d'Electrotechnique et d'Automatique JTEA 92
, Tunisia,
1992
, pp.
37
-
47
.
29.
Lu
,
F. S.
, “
Optimization of Quantization Based on rth-Power Distortion Measures
,”
IEEE Proceedings-F
, Vol.
136
, No.
6
,
12
1989
, pp. 276-282.
30.
Liang
,
Z.
and
Steinberg
,
B. D.
, “
Optimum Data Quantization in Microwave Imagery and Its Effects Upon Image Quality
,”
IEEE Trans. Acoust., Speech, Signal Process.
 0096-3518, Vol.
36
, No.
12
,
12
1988
, pp.
1889
-
1898
.
31.
Westerink
,
P. H.
,
Biemond
,
J.
, and
Boekee
,
D. E.
, “
Scalar Quantization Error Analysis for Image Subband Coding Using QMFs
,”
IEEE Trans. Signal Process.
 1053-587X, Vol.
40
, No.
2
,
02
1992
, pp.
421
-
428
.
32.
C-CUBE MICROSYSTEMS
, “
CL550 JPEG Image Compression Processor—Background Information
,”
02
1990
, pp.
5
-
7
.
33.
Truchetet
,
F.
, “
Ondelettes pour le signal numérique
,” Hermes Edition, Paris
1998
.
34.
Goupillaud
,
P.
,
Grossmann
,
A.
, and
Morlet
,
J.
, “
Cycle-Octave and Related transforms in Seismic Signal Analysis
,”
Geoexploration
 0016-7142 https://doi.org/10.1016/0016-7142(84)90025-5, Vol.
23
,
1984
, pp.
85
-
102
.
35.
Scholtz
,
P.
and
Gili
,
L.
, “
Dispersion Analysis by Wavelet TransformTailored for the Data
,”
EAGE 59th Conference and Technical Exhibition, Division of Geophysics
,
Geneva, Suisse
,
05
1997
.
36.
Kaoua
,
M.
,
Tighidet
,
M.
,
Herbeuval
,
J. P.
,
Yvroud
,
E.
, and
Flamant
,
Y.
, “
La transformée en ondelette appliquée à l'analyse des signaux cardiaques
,”
16èmes Journées Tunisiennes d'Electrotechnique et d'Automatique JTEA 96
, Tunisia,
11
1996
, pp.
440
-
443
.
37.
Fourati
,
W.
,
Kammoun
,
F.
, and
Bouhlel
,
M. S.
, “
Medical Image Denoising UsingWavelet Thresholding
,”
J. Test. Eval.
 0090-3973, Vol.
33
, No.
5
,
09
2005
, pp.
364
-
369
.
38.
Bouda
,
R.
,
Azamberti
,
Y.
,
Ferrand
,
D.
, and
Guillaume
,
M.
, “
Etude d'un descripteur de contour par la transformée en ondelettes
,”
16èmes Journées Tunisiennes d'Electrotechnique et d'Automatique
, Tunisia,
11
1996
, pp.
440
-
443
.
39.
Grossmann
,
A.
and
Morlet
,
J.
, “
Decomposition of Hardy Functions Into Square Integrable Wavelets of Constant Shape
,”
SIAM J. Math. Anal.
 0036-1410 https://doi.org/10.1137/0515056, Vol.
15
, No.
4
,
1984
, pp.
723
-
736
.
40.
Meyer
,
Y.
, “
Orthonormal Wavelets
,” in
Combes
J. M.
,
Grossman
A.
, and
Tchamitchian
P.
,
Wavelets, Time-frequency Methods and Phase Space
,
Spring
,
Berlin
,
1989
, pp.
21
-
37
.
41.
Mallat
,
S. G.
, “
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
,”
IEEE Trans. Pattern Anal. Mach. Intell.
 0162-8828 https://doi.org/10.1109/34.192463, Vol.
11
, No.
7
,
07
1989
, pp.
674
-
693
.
42.
Daubechies
,
I.
, “
Orthonormal Bases of Compactly Supported Wavelets
,”
Commun. Pure Appl. Math.
 0010-3640, Vol.
41
,
11
1988
, pp.
909
-
996
.
43.
Daubechies
,
I.
, “
The Wavelet Transform, Time-Frequency Localization, and Signal Analysis
,”
IEEE Trans. Inf. Theory
 0018-9448 https://doi.org/10.1109/18.57199, Vol.
36
, No.
5
,
09
1990
, pp.
961
-
1005
.
44.
Bouda
,
R.
,
Ferrand
,
D.
, and
Paquet-Campillo
,
V.
, “
Etude et propriétés des ondelettes en traitement du signal
,”
17èmes Journées Tunisiennes d'Electronique et d'Automatique, JTEA 97
, Tunisia,
11
1997
, pp.
114
-
123
.
45.
Adams
,
M. D.
and
Kossentini
,
F.
, “
Reversible Integer-to-Integer Wavelet Transforms for Image Compression: Evaluation and Analysis
,”
IEEETrans. Image Process.
, Vol.
9
, No.
6
,
2000
, pp.
1010
-
1024
.
46.
Nelson
,
M.
, “
La compression de données
,” Dunod Edition,
1993
.
47.
Rao
,
R.
, “
Wavelet Transforms: Introduction to Theory and Applications
,”
Addison-Wesley
,
Hardcover
, Bk&Disk Edition,
09
1998
, ISBN: 0-201-63463-5.
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