International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 5- May 2015
Design and Implementation of High Throughput
Memory Efficient Arithmetic Coder for Image
Compression Using SPIHT
Rabiya Khanum1, Asha R2
PG student (VLSI Design and Embedded systems), SIET, Tumkur, Karnataka, India.
Assistant Prof., Dept. of E&C, SIET, Tumkur, Karnataka, India.
Abstract-- A design is proposed based on the new coding
scheme for a novel image compression algorithm SPIHT (Set
Partitioning in Hierarchical tree) using wavelet transform and
arithmetic coder that provide an embedded code word. Image
compression using SPIHT attracts more interest due its low
memory requirement to represent an image. Due to its inherent
redundancy the algorithm is suitable for both color and gray
images. SPIHT display several important properties over other
image compression algorithm like fast coding and decoding, high
compression ratio, application in lossless image compression,
good image quality, high PSNR value and it has a capability to
code for exact bit rate. The speed of the SPIHT algorithm is
increased by using Arithmetic Coder. High speed architecture of
arithmetic coder is design to meet the throughput requirement
in order to achieve high performance gain. The design has been
implemented on Spartan 3 FPGA.
Keywords: Image Compression, Wavelet Transform,
Arithmetic Coder, Set Partitioning in Hierarchical Trees, Peak
Signal to Noise Ratio.
I. INTRODUCTION
As the demand for wireless communication and
multimedia product has been growing very fast, and the high
resolution images contain large amount information which
intern consume large amount of storage space and longer
transmission time. Therefore the theory of compression
becomes more important in the field of communication and
information industry for reducing the memory and
transmission time. Image Compression is the process
reducing the size of an image without much affecting the
quality of an image. The main objective of image
compression is to reduce redundancy of the image data in
order to store or to transmit the data in an efficient form.
Uncompressed form of multimedia data it may be audio or
video data requires considerable amount of storage space and
transmission time. The main objective of compression is to
provide sufficient storage space, less transmission time and
wider transmission bandwidth for video and audio data.
Image compression points at rejecting redundancy in image.
By dismissing the redundant information in an image help
image. Redundancy is nothing but dismissing or removing the
duplication in the image pixel.
Compression
techniques are generally classified into two types namely I)
lossy compression and II) lossless compression technique, in
ISSN: 2231-5381
lossy compression technique there is loss of information
hence after compression/ decompression the data is lost
forever, and recovered data (image) is not identical to its
original data (image). In this technique higher level of
compression can be achieved. This technique is useful in
some applications like television broadcasting, you tube,
video conferencing etc where certain amount of data loss can
be acceptable. Whereas in the lossless image compression
technique helps in providing compressed\decompressed form
of image which is digitally identical to original image. The
recovered data after decompression is identical to its original
data. This technique finds its application in medical field and
in technical drawings.
There are several different ways in which image files can
be compressed. For Internet use, the two most common
compressed graphic image formats are the JPEG format and
the GIF format. The JPEG method is more often used for
photographs, while the GIF method is commonly used for
line art and other images in which geometric shapes are
relatively simple. The rest of the paper is organized as
fallows, section II gives brief review on literature survey,
section III gives review on motivation and proposed
methodology, section IV description, section V. tests and
results, and finally the conclusion and future work of the
paper is presented in section VI and VII.
II. LITERATURE SURVEY
For many years, various architectures have been
proposed in order to achieve high compression ratio, high
PSNR ratio less transmission time, deal with such difficulties.
Andra’s [4] proposes a QM coder in JPEG which decreases
operation for the more probable symbol (MPS) and used a
non-overlap window style for the speedup purpose. In, the
probability interval partition’s accelerated by exchange of the
less probable symbol (LPS) interval with the MPS interval.
Thus the amount of operations is reduced by 60% to 70%
compared with other coders. Wheeler proposed a modified
SPIHT algorithm [5] which does not use any list. Because of
no search operations for list, the speed of algorithm can be
improved greatly. Wiseman proposed [6] hardware
architecture for a quasi AC which is a simple version of AC.
In this AC uses a pipeline processing to compute each stage,
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which eliminates an internal high frequency clock and utilizes
fast since [5] uses the pipeline processing, a fast lookup table
is utilized and also the high frequency clock is eliminated.
Although this architecture can improve the speed, it cannot
offer supports for multi-context processing in image
compression fields. A context based SPIHT method was
introduced by Ansari [9]. In [9], it is focused on achieving
better results in medical images not on hardware
implementation.
III. MOTIVATION & PROPOSED SYSTEM
One of the major challenges in enabling mobile,
multimedia data services will be the need to process and
wirelessly transmit a very large volume of data. While
significant improvements in bandwidth are expected with
future wireless access technologies, improvement in battery
technology will lag the rapidly growing energy requirements
of future wireless data services. One approach to mitigate this
problem is to reduce the volume of multimedia data
transmitted over the wireless channel via data compression
techniques. Proposed methodology reduces the volume of
data to greater extent. Methods involved in proposed system
are Discrete Wavelet Transform, SPIHT Algorithm, and
Arithmetic Coding.
IV. DESCRIPTION
A. Discrete Wavelet Transforms
Discrete Wavelet Transform is a wavelet transform in
which wavelets are discretely sampled. “Discrete Wavelet
Transform”, transforms discrete signal from time domain into
time-frequency domain. Since the input signal (e.g., a digital
image) is processed by a digital computing machine, it is
prudent to define the discrete version of the wavelet
transform.
A two-dimensional digital data can be represented by a
two-dimensional array A [X, Y] with X rows and Y columns,
where X and Y are nonnegative integers. The simple
approach for two-dimensional implementation of the DWT is
to perform the one-dimensional DWT row-wise to produce an
intermediate result and then perform the same onedimensional DWT column-wise on this intermediate result to
produce the final result. This is shown in Fig.2.
Fig. 2 Block diagram 2- D DWT
Fig. 1 Block diagram of proposed system with input and output
The block diagram of the SPIHT encoding for a proposed
system is described here. The input image is gray scale image
of size 512x512 each pixel of 8 bits. Input image is converted
to pixel values in MATLAB. The obtained Pixel values are
given as input to the Line based wavelet lifting module which
produces wavelet coefficients. The transformed wavelet
coefficients are placed in a buffer and they are accessed in a
SPIHT-Breadth First Search way. Processor dispatcher
dispatches the transformed wavelet coefficients to the
arithmetic coder through internal bus. Output of arithmetic
coder is provided to the internal bus and sent to the code
FIFO. The Read FIFO and Truncate module are responsible
for the final code stream formation, which reads each code
FIFO from top to bottom and truncates the code stream
according to the bit rate requirement. As shown in Fig 1.
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Fig. 3 Block diagram of Lifting-based Algorithm
Folded architecture for (9, 7) wavelet with line based
lifting wavelet engine is as shown in Fig .3. The z−1 blocks
are for delay; α, β, γ, δ, δ are lifting coefficients, and the
shaded blocks are registers to store the wavelet co efficient.
B. SPIHT Algorithm
SPIHT is the wavelet based image compression method.
It provides the Highest Image Quality, Progressive image
transmission. SPIHT makes use of three lists – the List of
Significant Pixels (LSP), List of Insignificant Pixels (LIP)
and List of Insignificant Sets (LIS). All the pixel values in the
list LIS are tested for their significant state. Significant state
of the wavelet coefficients are tested using the equation (1)
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 5- May 2015
which is as given below. Hence SPIHT algorithm has fewer
bits to code after the discrete wavelet transform. [4]. Where
Ci,j represents the coefficient value for the position i, j in the
wavelet sub-band. Г represents set of coefficients and Sn (Г)
represents the significant state of the set
Sn ( )
1, max (i , j )
ci , j
2n
(1)
0, otherwise
efficiency and more flexibility compared to the popular
Huffman coding.
The arithmetic coding algorithm is explained here with
an example. Consider a four-symbol alphabet A = {a, b, c, d}
with the fixed symbol probabilities p (b) = 0.3, p (a) = 0.2,
p(c) = 0.4, and p (d) = 0.1 respectively. The symbol
probabilities can be expressed in terms of partition of the
half-open range [0.0, 1.0), as shown in Table 2.
C. Flow Chart of SPIHT algorithm
Table 2 Probability Model
In this flow chart shown in Fig.4 the first method is to
perform wavelet decomposition on the loaded image of
512x512, the wavelet decomposition output is in the form of
sub bands. The sub band coefficients are given as the input
encoding stage. The encoding stage is divided into two parts.
The sorting pass
The refinement pass
In the first step that is sorting pass, we first initialize List
if significant pixel (LSP) to be empty and add the all
coordinates to List of insignificant pixel (LIP) and all the
decedents to List of insignificant set (LIS). Magnitude test is
Performed using equation (1); if the value is greater than
threshold moved that value to LSP else keep in LIS.
After the initialization, the algorithm takes two steps for
each level. The sorting pass (in which lists are organized)
and the refinement pass. The result obtained is in the form of
a bit stream.
Original image
Index
Symbol
Probability
1
2
3
4
b
a
c
d
0.3
0.2
0.4
0.1
Cumulative
probability
0.3
0.5
0.9
1.0
Range
0.0
0.3-0.5
0.5-0.9
0.9-0.1
“c b c a” is the new message to be encoded using the
above fixed arithmetic model. The first symbol of the
message is c, the range is first narrowed down to the halfopen interval R(c) = [0.5, 0.9). This range is again partitioned
into exactly the same proportions as the original one, giving
the four half-open intervals [0.5, 0.62). [0.62, 0.70), [0.70,
0.86), and [0.86, 0.90) corresponding to a, b, c. As a result,
the range is narrowed down to R(c b) = [0.5, 0.62) when the
second symbol a in the message is processed. The new range
[0.5, 0.62) is now partitioned into four equal intervals [0.5,
0.536), [0.536, 0.560), [0.560, 0.608), and [0.608, 0.62). After
the third symbol, is c processing, the range is accordingly
narrowed down to R(c b c) = [0.560, 0.608), like this way the
arithmetic coding is done.
Wavelet transform
The Architecture of Arithmetic Coder is shown in Fig.5
arithmetic coder consists of three main parts, upper and lower
bound update, and common bit detector. For updating the
initial intervals to 0 and 1, upper bound and lower bound
update of arithmetic coder is used. The values are multiplied
with cumulative probabilities and updated high and low
values are given as input to common bit detector unit. Output
is then passed to the code stream output unit in arithmetic
coder. Cumulative probability part will hold the frequency of
occurrence of wavelet coefficient.
Sorting pass
Refinement pass
Entropy coding
Figure 4: Flow Chart of SPIHT algorithm
D. Architecture of Arithmetic Coder
Arithmetic coding is a variable-length source encoding
technique. In traditional entropy encoding techniques such as
Huffman coding, each input symbol in a message is
substituted by a specific code specified by an integer number
of bits. Arithmetic coding deviates from this. In arithmetic
coding a sequence of input symbols is represented by an
interval of real numbers between 0.0 and 1.0. The longer the
message, the smaller the interval to represent the message
becomes. More probable symbols reduce the interval less than
the less probable symbols and hence add fewer bits in the
encoded message. Arithmetic coding offers superior
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Fig.5. Architecture of Arithmetic Coder
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 5- May 2015
The obtained new bound values are given as input to the
common bit detector (CBD) part which checks the internal
loop and records the duplicate bits from the MSB to the LSB
between two registers. [7] After that the same bits are
collected to code stream which is in the form of bits. These
bytes are supplied directly to the Code Stream Output part for
generating final code word.
V. TESTS AND RESULTS.
The Fig.8 shows the simulation results of arithmetic
coder. The design for arithmetic coder is done in verilog and
simulated using Xilinx ISI simulator.
In the experimental results first PSNR values for
different images is recorded using SPIHT with arithmetic
coder and it is compared with the existing system as shown in
the Table 2 using MATLAB.
Table 2. PSNR values of different images
Index
Images
512x512
PSNR value of
existing system
1
2
3
4
Lena
Barbara
Woman
Airport
38.39
36.01
37.37
33.27
PSNR value
of proposed
system
39.85
36.64
38.48
34.45
Probability Range
The design of DWT is described in verilog and testing of
this module has been carried out and simulation results of
DWT are shown in Fig.7. The input to this module is the
pixel values and output from this is the wavelet coefficient.
The RTL view of DWT is shown in Fig. 6.
Encoded data
Output
Fig.8 simulation results of arithmetic coder
The encoding is done for four symbols with the
predefined probability. The range is calculated for each
symbol using that predefined probability, and the encoded
data is as shown in the Fig.8.
The Fig.9 shows the results of SPIHT-Arithmetic coder.
The PSNR value of the Lena image is given below.
Fig.6 shows RTL View of DWT
PSNR value of Lena image
Fig.9 MATLAB results of entire design
Output
Input
Fig.7. Simulation results of DWT
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Figure 10 shows the simulation output of image
compression using DWT in MATLAB software. Gray scale
image of 512X512 is given as input.2-D DWT is first applied
on rows and then on the columns.
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 5- May 2015
Fig. 12 Output obtained on Chipscope Pro window of Xilinx 14.5 ISE
VI. CONCLUSION
Fig.10 MATLAB results image compression
The design is implemented on Spartan 3 FPGA and
the design is described using verilog and MATLAB software
and it is synthesized and the output is observed on Chipscope
Pro Window, the option available in Xilinx ISE 14.5 software
for analyzing the hardware results Fig. 12 shows output of the
design obtained on Chipscope Pro Window.
An effective VLSI implementation of image compression
is proposed in this design. The hardware is realized on
Spartan 3 FPGA kit. Output of the design is observed on
ChipScope Pro window in Xilinx ISE 14.2. The results make
the following conclusions as given below:1) The combination of DWT and SPIHT gives better image
quality at low bit rate and at the same time performance of the
design is improved.
2) Around 76.8% of compression ratio can be obtained using
this design. Hence the memory required for the storing the
data will be less.
3) The SPIHT with arithmetic coder improves the peak signal
to noise ratio.
From the above observation the proposed design can be
concluded as smaller storage space is needed to store the
encoded bit-stream and it is easy to transmit encoded bitstream in lesser transmission bandwidth.
VII. FUTURE WORK
Fig. 11 Simulated output of DWT
For improvement of throughput purpose SPIHT
algorithm without lists can be implemented. A simple context
scheme can be employed. A simple context scheme can be
used in future especially to reduce the power required by
multimedia data while transferring data from one end to
another end, control module can reduce the power dissipation
efficiently as the reduction in power consumption leads to
higher battery life in the portable devices.
ACKNOWLEDGMENT
I am thankful to Dr. Nalini. N, Principal, SIET, Tumkur
for her valuable guidance was a source of inspiration. I
express my gratitude to Dr M.N Eshwarappa professor and
HOD Dept of E&C SIET, Tumkur, for providing motivation
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 5- May 2015
and required support for completing this project. I am grateful
to Mrs. ASHA.R Assistant professor Dept of E&C SIET
Tumkur, for her esteemed and valuable guidance and
encouragement and lending every support at every stage of
this project work and accepting to be my internal guide.
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