Non standard size image compression with reversible embedded wavelets

IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
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Volume: 01 Issue: 03 | Nov-2012, Available @ http://www.ijret.org 378
NON STANDARD SIZE IMAGE COMPRESSION WITH REVERSIBLE
EMBEDDED WAVELETS
Abdul Sattar
Assistant professor, Electronics & Telecommunication Engineering Department, B. N. College Of Engineering PUSAD
shaikhsattar@rediffmail.com
Abstract
The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing and high definition
television, (HDTV) has increased the need of effective image processing. While processing any data, it requires large memory space
for storage, which ultimately increases the transmission time. In order to save memory space and speed up the rate of transmission of
data over networks, data compression is essential. Technically all image data Compressed into two groups as lossless and lossy. Some
information is lost in the lossy compression, especially for radiological images. In this paper Non standard size still images are
compressed by CREW using MATLAB. It uses a new form of wavelet transform technology. It is pyramidal (similar to hierarchical)
and progressive by nature. From results it is observed that CREW provides higher compression ratio as compared to JPEG
compression with same quality of image. The PSNR is also in acceptable range.
The features make CREW an ideal choice for applications that require high quality and flexibility for multiple input and output
environments, such as, medical imagery, fixed-rate and fixed-size applications.
Keywords– CREW, JPEG, Image Compression, JPEG2000
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1. INTRODUCTION
Uncompressed multimedia data (graphics, audio and video)
requires considerable storage capacity and transmission
bandwidth. Despite of rapid progress in mass storage density,
processor speeds, and digital communication system
performance, demand for data storage capacity and data-
transmission bandwidth continues to outstrip the capabilities
of available technologies. The recent growth of data intensive
multimedia based applications have not only sustained the
need for more efficient ways to encode signals and images but
have made compression of such signals central to storage and
communication technology [1].
For still image compression, the JPEG [2] standard has been
established. The JPEG compression encoding is based on
Discrete Cosine Transform [3] scheme. First the image is
divided into 8 x 8 block size and then DCT is applied. Due to
this block based DCT scheme, the performance of these
encoders generally degrades at low bit rates.
Over the past few years, a variety of powerful and
sophisticated scheme for image compression with high
compression ratio and good image quality have been
developed and implemented. More recently, the wavelet
transform has emerged as a cutting edge technology. Wavelet
based coding [4] provides substantial improvements in picture
quality at higher compression ratios. This paper introduces
some basic concepts on image compression and the more
popular wavelet based image-coding schemes. Further the
performance of wavelet-based compression is compared with
JPEG compression.
In this paper section (II) describes image compression
techniques using CREW. In section (III) the algorithm
implemented is described. In section (IV) experimental results
of wavelet transform are given. The performance comparison
is briefed in section (V) and section (VI) concludes the paper.
2. COMPRESSION WITH REVERSIBLE
EMBEDDED WAVELETS
CREW is a completely new type of image compression
system. CREW is the first lossless and lossy continuous-tone
still image compression system. It is based on a lossless
reversible wavelet transform and has embedded quantization
before storing and transmitting the mage. To reconstruct the
compressed image, it is decoded, dequantized and inverse
transformed.
A. Reversible Wavelets
A reversible transform is an implementation of an exact
reconstruction transform in integer arithmetic, such that a
signal with integer coefficients can be losslessly recovered. An
efficient reversible transform is one with transform matrix [5]
of determinant≈ 1[6].There are two reversible wavelet

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transforms are employed. The first one, the so-called S-
transform is introduced in and used by and [6] among others.
The second one, the TS-transform was introduced in [7].
Let x(0),x(1),x(2),….. be the input signal, and let
s(0),s(1),…..and d(0),d(1),……. be the smooth and the detail
outputs respectively. The smooth output and the detail output
are the results of the applications of the low-pass and the high-
pass filters respectively.
The S-transform: The S-transform is defined by the outputs
at a given index, n, is given in equ. (a).
s(n)= └x(2n)+x(2n+1)┘
2
(a)
d(n)= x(2n)-x(2n+1)
2
The factor of two in the transform coefficients addressing is
the result of an implied subsampling by two. This transform is
reversible and the inverse is given in equ. (b).
x (2n) = s(n) +└ d(n) +1┘
2
(b)
x (2n+1)= s(n)- └ d(n) ┘
2
The TS-transform: Similar to the S-transform, the TS-
transform or two-six transform named after the number of taps
in the low and high pass respectively
B. Embedded Quantization
Lossy compression is achieved by embedded quantization.
Embedded is used here to indicate that the codestream
includes the quantization. The actual quantization (or visual
importance) levels can be a function of the decoder or the
transmission channel, not necessarily the encoder.
C. Pyramidal and Progressive Transmission
The CREW wavelet is pyramidal. Here pyramidal refers to a
decomposition by a factor of two of the image without
difference images. Here progressive refers specifically to
progressive by bit-plane, i.e. MSB followed by lessor bits.
Both the spatial and wavelet domains can be decomposed
progressively, although CREW is progressive in the wavelet
domain specifically.
D. Tree Structure of Wavelet Decomposition
Figure.(1) shows a diagram of a wavelet decomposed image.
The first level of coefficients is in the bottom and right most
quadrants. These are denoted by LL, HL, HH, LH
corresponding to high pass horizontal and low pass vertical,
high pass horizontal and high pass vertical, low pass
horizontal and high pass vertical respectively. The LL part of
the first level is again decomposed, and so on. There is a
natural and useful tree structure to wavelet coefficients in a
pyramidal decomposition. Note that, there is a single LL
subblock corresponding to the last level of decomposition. On
the other hand there are as many HL, LH, and HH bands as the
number of levels. The tree structure first introduced by Lewis
and Knowles [8] and shown in figure (2), the coefficient at A
is the direct parent to B, C and D and all their decedents.
Specifically B is the parent to the four coefficients around E
and the sixteen coefficients around H, etc
Figure.1Relationship between the coefficients
Figure.2 Tree Structure

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E. Ordering Of The Coefficients And Bit Planes
The ordering of the data is important to realize the embedded
quantization of the codestream. Two ordering systems are
required: one for ordering the coefficients and the second for
ordering the binary values within a coefficient. This order
leads to a bitstream that is coded with a binary entropy coder.
All the coefficients within a coding unit are available in the
random access memory, the embedding order between the
coefficients within a coding unit can be any arbitrary order,
known to both the encoder and the decoder. But since the
entropy coder must be causal with respect to this ordering, it
has a significant impact on the compression.
The embedded order used within a coefficient is bit-
significance in the transform domain which is similar to but
more general than the system used in [9]. The largest possible
coefficient is used as a reference, and the coefficients are
aligned with respect to it. This alignment is near-optimal in
terms of statistical error metric such as MSE. Other
alignments could correspond to coefficient specific
quantization.
The binary entropy coder uses a Horizon context model in
order to encode the coefficients. The model uses bits within a
coding unit based on the spatial and spectral dependencies of
the coefficients. The available binary values of the
neighboring coefficients and parent coefficients can be used to
create contexts. The contexts however must be causal for
decidability and in small numbers for efficient adaptation.
F. Entropy Coding
The bit stream is encoded with a binary entropy coder. For this
implementation Q-coder is used.
3. ALGORITHM
1) Digitize the source image into a signal s, which is a string
of numbers.
2) Decompose the signal into a sequence of wavelet
coefficients w.
3) Use thresholding to modify the wavelet coefficients
4) Use quantization to convert w' to a sequence q.
5) Apply entropy coding to compress q into a sequence
4. EXPERIMENTAL RESULTS
5. PERFORMANCE COMPARISON CREW
Table 1: Compression Ratios and PSNR using
CREW
From the images of the experimental results it is seen that in
JPEG method the effects of artifacts are due the correlation
between boundaries of the blocks of the DCT
CONCLUSIONS
Over the past several years, the wavelet transform has gained
widespread acceptance in signal processing in general, and in
image compression research in particular. In many
applications wavelet-based schemes (also referred as subband
coding) outperform other coding schemes like the one based
on DCT. Since there is no need to block the input image and
its basis functions have variable length, wavelet coding
schemes at higher compression avoid blocking artifacts.
Wavelet-based coding is more robust under transmission and
decoding errors, and also facilitates progressive transmission
of images. In addition, they are better matched to the HVS
characteristics. Because of their inherent multiresolution
nature[4], wavelet coding schemes are especially suitable for
applications where scalability and tolerable degradation are
important.
The CREW based image compression techniques provide
higher compression ratios with moderate PSNR. The picture
quality is also good for the intended application. The
upcoming JPEG- 2000 standard incorporates the inherent
multiresolution nature of wavelet transform. Many methods
like EZW [6], SPIHT [7], EBCOT [8], SR [9] utilizes the
wavelet image coding using decomposition techniques. There
are few outstanding challenges facing the data compression
community like interaction of harmonic analysis with data
compression, joint source channel coding, image coding based
on models of human perception, scalability, robustness, error
resilience, and complexity. The challenges after fully resolved
may enhance image data compression performance in the
years to come.
Images Level MSE PSNR
dB
C R% En-tropy
face1 3 7.95 39.13 87.50 7.03
dog 3 0.89. 48.64 75 7.17
flower 3 1.27 37.25 87.5 6.76
egret 3 0.13 57.07 75 6.92
bird 3 1.48 46.44 75 7.74

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REFERENCES
[ 1 ] Subhasis Saha, “Image compression – from DCT to
Wavelets: A review”, ACM crossroads student
magazine.
[ 2 ] Pennebaker, W. B. and Mitchell, J. L. JPEG - Still
Image Data Compression Standards, Van Nostrand
Reinhold, 1993
[ 3 ] Rao, K. R. and Yip, P. Discrete Cosine Transforms -
Algorithms, Advantages, Applications, Academic Press,
1990.
[ 4 ] Vetterli, M. and Kovacevic, J. Wavelets and Subband
Coding, Englewood Cliffs, NJ, Prentice Hall, 1995.
[ 5 ] J. Shapiro, “An embedded wavelet hierarchical image
coder,” Proc. IEEE Int. Conf. Acoust., Speech, Signal
Proc., vol. IV, pp. 657–660, March 1992.
[ 6 ] M. J. Gormish and J. Allen, “Finite state machine
binary entropy coding,” in Proc. Data Compression
Conference, (Snowbird, Utah), p. 449, March 1993.
Abstract only, full text available as Ricoh California
Research Center Technical
[ 7 ] J. Villasenor, B. Belzer, and J. Liao, “Filter evaluation
and selection in wavelet image compression,” in Data
Compression Conference, (Snowbird, Utah), IEEE,
1994.
[ 8 ] E. Simoncelli and E. Adelson, “Subband Transforms,”
in Subband Coding (J. Woods, ed.), ch. 4, Norwell,
Massachusetts: Kluwer Academic Publishers, 1990.
[ 9 ] A. Zandi, J. D. Allen, E. L. Schwartz, and M. Boliek,
“CREW: Compression with reversible embedded
wavelets,” in Data Compression Conference,
(Snowbird, Utah), pp. 212–221, IEEE, March 1995.

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