In this technical article, we present a Novel algorithm for the lossy compression method, where the performance and storage has been proscribed with hardware descriptive language (HDL).

1. A Novel Algorithm Towards Lossy Image Compression Using
FPGA
By K. RAJESH KUMAR, Design Engineer,
Mistral Solutions Pvt. Ltd., Bangalore, India
Abstract
Due to the advancement of technology in medical and security, there is a prerequisite for huge storage of image .The performance and
the storage area are the main challenge towards the compression and decompression of the image. In this paper we have presented a
Novel algorithm for the lossy compression method, where the performance and storage has been proscribed with hardware descriptive
language (HDL). In addition MSE (Mean Squared Error), PSNR (Peak Signal to Noise Ratio), Power and Area has been calculated and
compared with various fractal compression algorithms.
Keywords: Lossy Image Compression, FPGA, HDL, MSE, PSNR.
I. INTRODUCTION
With the advance of technology in recent year, compelled us to
use image compression in numerous areas like medical and
security .Basically a image is a sequence of weighted data . The
reduction of strength or the data storage leads to compression of
a image.
As a broader classification the compression has been divided
into lossy and lossless compression. Here we deal with lossy
compression.
The Lossy compression is a data encoding method that
compresses data by discarding (losing) some of it. The
procedure aims to minimize the amount of data that needs to be
held, handled, and/or transmitted by a computer.
Types of Lossy Compression
There are three major types of lossy data compression technique.
They are as follows:
1. Lossy transform codecs
2. Lossy predictive codecs
3. Chroma subsampling
Let us now discuss these types of lossy compression in detail.
1. Lossy transform codecs
The lossy transform codecs compression is generally used for
JPEG images only. In this case samples of the picture is taken,
they are then choped into smaller segments and then transformed
into a new image. The resulted image has fewer colors than its
original, hence decreasing its quality.
2. Lossy predictive codecs
In predictive codecs, previous and/or subsequent decoded data is
used to predict the compressed image frame.
3. Chroma subsampling
Chroma subsampling is another type of lossy compression that
takes into account that the human eye perceives changes in
brightness more sharply than changes of color, and takes
advantage of it by dropping or averaging some chroma (color)
information while maintaining luma (brightness) information.
It’s commonly used in video encoding schemes and in JPEG
images. At some places the above two techniques are combined
to compress the image in a better way.
This paper presents a new algorithm for lossy compression and
compared with the existing techniques like the standard LMS,
the normalized LMS (NLMS),the MVSS, the conventional
TDLMS, the DCT-LMS, the TDVSS, and the VSSTDLMS.
Several existing compression scheme are analyzed in section II.
The proposed method is described in detail in section III. Then
the performance comparisons are described in section IV.
Finally the conclusion is given in the section V.
II. Analysis of existing method:
Tyseer Aboulnasr and K. Mayyas presented a robust variable step-
size LMS-type algorithm[1] providing fast convergence at early
stages of adaptation while ensuring small final misadjustment. The
performance of the algorithm is not affected by existing
uncorrelated noise disturbances. An approximate analysis of
convergence and steady-state performance for zero-mean stationary
Gaussian inputs and for non-stationary optimal weight vector is
provided.
S.Shankar,Allen m.peterson and Madihally [2]explained that
filtering in the transform domain results in great improvements in
convergence rate over the conventional time domain adaptive
filtering.
K.Mayyas performed analysis of the DCT-LMS adaptive
filtering algorithm [3] and showed how the integrity has to be
preserved and in there another paper “Mean-Square Analysis of
a Variable Step She Transform Domain LMS Adaptive
Algorithm”[5] presented MSE analysis of a new variable step
size TDLMS algorithm. Analysis has yielded a set of difference
equations that describe the mean square behavior of the

2. algorithm, and a formula for the steady state excess MSE was
derived. Steady state MSE analysis, supported by experimental
results, indicated that the algorithm misadjustment essentially
depends on with a very little effect of the input signal statistics
and the adaptive filter length. Consequently, the algorithm
steady state performance can easily be predicted with the
knowledge of . Radu Ciprian Bilcu, Pauli Kuosmanen, and
Karen Egiazarian in there paper” A Transform Domain LMS
Adaptive Filter With Variable Step-Size”[4] introduced a new
transform domain (least mean square)LMS algorithm with
variable step . The step-sizes are time-variable due to the power
estimates of each transform coefficient. In there approach, for
each step-size they defined a local component that is given by the
power normalization, and a global component that is the same for
each filter coefficient.
III. The proposed Image Compression Method
Figure 1: Block Diagram of Proposed Scheme
The strength of the weighted data in the image has been reduced
by subtracting all the data’s with the matrix mean and made into
small clusters .The each clusters are parallel processed by taking
the threshold and dividing it into smaller module’s and assigned
a weighted value (refer the example 1.1 for more details) . These
individual clusters are concatenated and in the DCT, the
concatenated image is divided into 8-by-8 or 16-by-16 blocks,
and the two-dimensional DCT is computed for each block. The
DCT coefficients are then quantized, coded, and stored in the
memory as compressed image .the forward steps are reversed to
get the lossy image. Figure 1, 2 and 3 represents the original,
compressed and reconstructed image.
Figure 2: Original image
Figure 3: Compressed Image
Figure 4: reconstructed image
An example for the proposed scheme:

3. IV. Performance comparison
In this section the proposed algorithm SME is compared with
the existing techniques like the standard LMS,the normalized
LMS (NLMS),the MVSS, the conventional TDLMS, the DCT-
LMS, the TDVSS, and the VSSTDLMS. The DCT was selected
as the orthogonal transform for all the simulations.
The following highly correlated input signal same as given in
[9]-[11] was used
Where v (n) is uncorreleated Gaussian signal with zero mean
and 0.14817 variance.
1. MSE
The MSE is the cumulative squared error between the
compressed and the original image
Given a noise-free m×n monochrome image I and its noisy
approximation K, MSE is defined as:
The MSE of the proposed algorithm is 0.0038910(signal
iteration)
.
Figure 5: MSE COMPARISION
Mean-square signal to noise ratio SNRms
The is the input image and the is the
compressed image where as M and N are the rows and column
of the matrix.
The SNRms of the proposed algorithm is 1.
2. PSNR
The PSNR is a measure of the peak error.
The PSNR is defined as:
Here, MAXI is the maximum possible pixel value of the image
The PSNR of the proposed algorithm is 1.1090355e+002.
The surface area plot
Figure 6: Surface Plot of Original Image
Figure 7: Surface Plot of Compressed Image
The figure 5. and figure 6. Shows the surface plot of original
and compressed image. The Z-Axis of original image is

4. weighted upto 253, where as the compressed image maximum
weight is 1.
V. Conclusion
In this paper, we have proposed a noval algorithm and compared
with the standard LMS,the normalized LMS (NLMS),the
MVSS, the conventional TDLMS, the DCT-LMS, the TDVSS,
and the VSSTDLMS .with the proposed algorithm when the
number of iteration increases, the MSE and the resolution
reduces where as the lookup table (threshold pool)size is
increasing. From the Figure 5 we can justify that the proposed
algorithm is better than LMS,NLMS and MVS in terms of MSE.
Reference
[1] Tyseer Aboulnasr, and K. Mayyas , “A Robust Variable
Step-Size LMS-Type Algorithm: Analysis and Simulations”
, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL.
45, NO. 3, MARCH 1997
[2] S.SHANKAR NARAYAN, ALLEN M. PETERSON and
MADIHALLY J. NARASIMHA, “Transform Domain LMS
Algorithm” , IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND
SIGNAL PROCESSING, VOL. ASSP-31, NO. 3, JUNE 1983
[3] K. Mayyas , Irbid and Jordan ,a note on “Performance
analysis of the DCT-LMS adaptive filtering algorithm”,
journal, signal processing volume 85 issue 7 July 2005
[4] Radu Ciprian Bilcu, Pauli Kuosmanen, and Karen Egiazarian ,
“A Transform Domain LMS Adaptive Filter With Variable
Step-Size” , IEEE SIGNAL PROCESSING LETTERS, VOL.
9, NO. 2, FEBRUARY 2002
[5] K. Mayyas , “Mean-Square Analysis of a Variable Step She
Transform Domain LMS Adaptive Algor it hm”
[6] Zhao Shengkui, Man Zhihong and Khoo Suiyang, “A New
Variable Step-Size Transform Domain LMS Algorithm
with System Identification” , IEEE International Conference
on Control and Automation Guangzhou, CHINA - May 30 to
June 1, 2007
[7] K. Mayyas, “A transform domain LMS algorithm with an
adaptive stepsize equation,” The 4th IEEE International
Symposium on Signal Processing and Information Technology
ISSPIT' 2004, Italy, Rome,Dec. 28-30, 2004.
VI. About the Author:
K. Rajesh Kumar received M.Tech in VLSI design from
Karunya University in 2011 and B.E in Electronics and
Communication Engineering from Anna University. He finished
Diploma in Electronics and Communication Engineering in
2006 and subsequently did Diploma in Information Technology
and Advanced Diploma in Information Technology in 2005. He
is currently working with Mistral Solutions as a Design
Engineer. He has published various papers in national and
international journals. He has successfully completed many
projects in Image Broadcasting and video processing. His
research interest includes Image Compression, Low power VLSI
and Cryptography.
(This article was featured on EDN Asia in April 2013)