Image compression using dpcm with lms algorithm ranbeer

IMAGE COMPRESSION USING DPCM
WITH LMS ALGORITHM
Guided by
Prof. Mr. Shekhar Sharma
Prof. Dr. B. Sarkar
Presented by
Ranbeer Tyagi
M.E. Final Sem.(E&TC)
11

Contents
 Introduction
 What is an Image
 Image Representation
 Basic step of an Image Compression
 Image Compression Problem and Solution
 Working of DPCM with LMS algorithm
 DPCM Quantization
 Adaptive Filtering Algorithm
 Simulation Results
 Conclusion
 Future Work
 References 22

Introduction
In general the reduction of image data is achieved by the
removal of redundant data. In mathematics, compression may
be defined as transforming the two-dimensional pixel array into a
statistically uncorrelated data set. Usually image compression is
applied prior to the storage or transmission of the image data.
Later the compressed image is decompressed to get the original
image or close to original image.
The LMS algorithm may be used to adapt the coefficients of an
adaptive prediction filter for image source encoding. Results are
presented which show LMS may provide almost 2 bit per pixel
reduction in transmitted bit rate compare to DPCM fixed
coefficient when distortion levels are approximately the same for
both methods.
33

 An image is an array, or a matrix, of square pixels (picture
elements) arranged in columns and rows.
Original Image
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100
150
200
250
F(x, y)
What is an Image
(0, 0)
x
y
44

Image Representation
 An image defined in the "real world" is considered to be a function of two real
variables, for example, f(x, y) with f as the amplitude (e.g. brightness) of the image
at the real coordinate position (x, y).
 The 2D continuous image f(x, y) is divided into N rows and M columns. The
intersection of a row and a column is called as pixel. The value assigned to the
integer coordinates [m, n] with{m=0,1, 2,...,M-1} and {n=0,1,2,...,N-1}is f[m,
n].In fact, in most cases f(x, y) which we might consider to be the physical signal
that impinges on the face of a sensor. Typically an image file such as BMP, JPEG,
TIFF, PNG etc.
 Figure shows the Each pixel has a value from 0 (black) to 255 (white).
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Basic step of an Image Compression
1. Specifying the rate (bits available) and distortion
(tolerable error) parameters for the target image.
2. Dividing the image data into various classes, based
on their importance.
3. Dividing the available bit budget among these
classes, such that the distortion is a minimum.
4. Quantize each class separately using the bit
allocation information derived in step 3.
5. Encode each class separately.
66

Image Compression Problem and
Solution
 Image compression with the help of DPCM for 3 bit .In this
method less reduction and more distortion . It is problem of
Image compression.
 Solution is to develop an algorithm for reducing the number
of bit and distortion.
 LMS may provide almost 2 bit per pixel reduction in
transmitted bit rate compare to DPCM when distortion levels
are approximately the same for both method.
77

Working of DPCM with LMS
algorithm
( )e n
∑ Q
LMS
Predictor
∑
Predict and compare loop
Predict and correct loop
Figure : Block Diagram of image compression using DPCM with
LMS Algorithm
88
e(n)
y(n)
+
+
+
-

DPCM Quantization
 The estimation residual
 The quantized to yield
Where q(n) is the quantization error , quantized signal.
And
 In DPCM we transmit not the present sample x(n), but e(n) is the
difference between x(n) and its predicted value y(n).
e(n)
99
Here b is number of bit is an image signal.
The prediction output y(n) is fed back to its input so that the predictor input is

Adaptive Filtering Algorithm
 In an image processing a model of the N taps predictor may
vary continuously hence the model needs to be updated
continuously. This is done by means of adaptive filtering
algorithms. The adaptive algorithm adjusts the weight
coefficients in the filter to minimize the estimation error .
 Common adaptive algorithms include the Least Mean
Square (LMS) Algorithm.
1010

LMS Algorithm
The LMS algorithm minimizes the expected value of the squared
error and Distortion.
µ is known as the step size parameter and is a small positive constant.
For stability
T
T
0 < µ <
1111

Flow Chart of the DPCM System
Quantization
1212
Initialization of the fixed two-tap-weight
Get the value of
Filter according to
Compute the error
Compute the quantize signal
+

Flow Chart of DPCM with LMS Algorithm
Ge
t
h
e
al
ue
f
Quantization
1313
Get the value of
Filter according to
Compute the error
Compute the quantize signal
Initialization of N - tap - weight
Updating the coefficient
+

Necessity for Better Performance of
Image Compression
 The selection of step size should be done
carefully to achieve More compression and
less steady state error.
 The number of Taps in the filter should be
large enough to cover the image path.
1414

Simulation Setup
 Mat lab 7.5
 Parameter use in Simulation
Average square distortion
Prediction mean square error
1515

Simulation Parameters
Parameter value
Image Matrix size 256×256
Original Image size 96.5 kB (98,915 bytes)
DPCM 1bit/pixel reconstructed Image size 83.0 kB (85,075 bytes)
DPCM 3bit/pixel reconstructed Image size 88.1 kB (90,243 bytes)
DPCM fixed Tap’s 2
DPCD weight coefficient value W=[0.495, .456]
No of Bit’s 1, 2, 3 bit’s
Quantization level 2, 4, 8 level
TABLE-1parametervalue/ Configuration of DPCM
Parameter Value
Image Matrix size 256×256
Original Image size 96.5 kB (98,915 bytes)
LMS 1bit/pixel reconstructed Image size 73.2 kB (74,960 bytes)
LMS 3bit/pixel reconstructed Image size 85.5 kB (87,618 bytes)
No of Filter Tap’s 420
LMS adaptive weight coefficient W=[ones(1,tap’s)]
No of Bit’s 1, 2, 3 bit’s
Quantization level 2, 4, 8 level
LMS Parameter µ=.0005
TABLE-2 parameter value /Configuration of using DPCM with LMS Algorithm
1616

0
100
200
300
400
500
600
700
800
Original Image histogram
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oimg
1717

0
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600
800
1000
1200
1400
histogram using DPCM
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1 bit/pixel
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0
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400
500
600
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800
histogram using DPCM
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3 bit/pixel
1919

0
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400
600
800
1000
1200
1400
1600
histogram using DPCM with LMS
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1bit/pixel
2020

0
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400
500
600
700
800
histogram using DPCM with LMS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
3bit/pixel
2121

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
-23.4
-23.2
-23
-22.8
-22.6
-22.4
-22.2
-22
-21.8
-21.6
-21.4
Average square distortion versus transmitted bit rate
AverageSquareDistortion[dB]
bit/pixel
DPCM
LMS
2222

Compressed image
(a) 3 bit/pixel LMS (DL= -22.4dB)
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Compressed image
(b) 3 bit/pixel DPCM (DL=- 22.25dB)
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Compressed image
(c) 1 bit/pixel LMS (DL= -23.3dB)
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Compressed image
(d) 1 bit/pixel DPCM (DL= -21.75dB)
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Figure: Visual results for processing Lena image with LMS and DPCM 2323
Original Image
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100
150
200
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0 50 100 150 200 250 300
-50
-45
-40
-35
-30
-25
Comparision of PMSE
PMSE[dB]
sample number
1bit/pixelLMS
1bit/pixelDPCM
2424

0 50 100 150 200 250 300
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
Comparision of PMSE
PMSE[dB]
sample number
3bit/pixelLMS
3bit/pixelDPCM
2525

Conclusion
 A comparison on using DPCM and using DPCM with
LMS algorithm with respect to image compression has
been carried out based on their coefficient and the
number of bits. The results show that the LMS algorithm
has the least computational complexity.
 Results are presented which show LMS may provide
almost 2 bits/pixel reduction in transmitted bit rate
compared to DPCM when distortion levels are
approximately the same for both methods.
2626

Future Work
 The test of the algorithm was performed totally ‘off-line’.
The testing image was saved before as input to the
algorithm and the output was looked over after
simulation. Therefore, the real-time application for
testing purpose could be the most interesting future work.
 Besides that, the image compression can be done with the
help of other adaptive filtering algorithm such as NLMS
and RLS. This work carried out in future.
2727

Reference
 S.Haykin and T.Kailath “Adaptive Filter Theory ” Fourth Edition.
Prentice Hall, Pearson Education 2002..
 S. ANNADURAI and R. SHANMUGALAKSHMI “Fundamentals of
digital image processing” Published by Dorling Kindersley (India)
2007.
 A. Habbi, “Comparison of Nth-order DPCM encoder with linear
transformation and block quantization techniques,” IEEE Trans.
Commun., vol. COM-19, pp. 948-956, Dec. 1971.
 S. T. Alexander and S. A. Rajala, “Analysis and simulation of an
adaptive image coding system using the LMS algorithm,” in Proc.
1982 IEEE Int. Conf. Acoust., Speech Signal Processing, Paris,
France, May 1982.
 KMM et al., Design and Fabrication of Color Scanner, Indian Journal
of Technology, Vol 15, Apr 1997. 28 2828

 Fundamentals Of Digital Image Processing - Anil K. Jain,
Prentice-Hall, 1989.
 Digital Image Processing - R.C. Gonzalez Woods, Addison
Wesley, 1992
 B. P. Lathi and Zhi ding “Modern Digital and Analog
Communication Systems” International Fourth Edition. New
York Oxford University Press-2010, pp.292.
 J. R. Zeidler et al., “Adaptive enhancement of mulyiple
sinusoids in uncorrelated noise,” IEEE Trans. Acoust., Speech,
Signal Processing, vol. ASSP-26, pp. 240-254, June 1978.
 J. E. Modestino, and D. G. Daut, “Source-channel coding of
images,” IEEE Trans. Commun., vol. COM-27, pp. 1644-1659,
Nov. 1979.
 W. K. Pratt, Digital Image Processing. New York: Wiley, 1978.
 M. D. Paez, and T. H. Glission, “Minimum mean square error
quantization in speech PCM and DPCM system,” IEEE Trans.
Commun. Vol. COM-20, pp. 225-230, Apr. 1972. 2929

Image compression using dpcm with lms algorithm ranbeer

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