Enhancing Image Quality in Compression and Fading Channels A Wavelet Based Approach with Db2 and De noising Filters

International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 8 Issue 2, March-April 2024 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD64684 | Volume – 8 | Issue – 2 | Mar-Apr 2024 Page 415
Enhancing Image Quality in Compression and Fading Channels:
A Wavelet-Based Approach with Db2 and De-noising Filters
Shreyaskumar Patel
Sr. Embedded Software Engineer, Department of R & D Platform, Netscout Systems, Allen, Texas, United States
ABSTRACT
The relentless growth in digital image data and its widespread
application across various fields such as medical imaging, satellite
imaging, and online content delivery necessitates efficient
compression techniques to reduce storage requirements and facilitate
faster transmission. However, traditional compression methods often
lead to a significant degradation in image quality, particularly at high
compression ratios, making the recovery of the original image
fidelity challenging. This paper investigates the impact of
compression ratio and PSNR on image quality, utilizing the 256×256
as a test image. It introduces a novel technique combining discrete
wavelet transforms with Db2 wavelet and various de-noising filters
(Wiener, Median) to enhance decompression quality measures, such
as SNR and BER, over existing methods. Further exploration is
conducted on the effect of increasing compression ratios on image
quality in flat fading channels using QPSK and 8-PSK modulation
techniques with the Db2 wavelet transform. Comparative results
demonstrate the efficacy of the proposed technique in maintaining
higher quality in decompressed images. This study not only
underscores the trade-off between compression ratio and image
quality but also showcases the potential of Db2 wavelet transforms in
improving performance in fading channel conditions for different
modulation schemes.
KEYWORDS: Image Compression, Discrete Wavelet Transform, Db2
Wavelet, De-noising Filters, SNR and BER, Flat Fading Channels,
QPSK and 8-PSK Modulations
How to cite this paper: Shreyaskumar
Patel "Enhancing Image Quality in
Compression and Fading Channels: A
Wavelet-Based Approach with Db2 and
De-noising Filters"
Published in
International Journal
of Trend in
Scientific Research
and Development
(ijtsrd), ISSN: 2456-
6470, Volume-8 |
Issue-2, April 2024, pp.415-422, URL:
www.ijtsrd.com/papers/ijtsrd64684.pdf
Copyright © 2024 by author (s) and
International Journal of Trend in
Scientific Research and Development
Journal. This is an
Open Access article
distributed under the
terms of the Creative Commons
Attribution License (CC BY 4.0)
(http://creativecommons.org/licenses/by/4.0)
1. INTRODUCTION
Image Compression has been the major area of
research because of the increasing demand for visual
communications in entertainment, medical and
business application over the existing band limited
channels. For image compression, it is very necessary
that the selection of transform reduce the size of the
resultant data as compared to the original data set
[1,2]. Image processing for a wireless transmission is
a challenging task because of the amount of image
data that need to be processed in real time having the
restriction of transmission bandwidth and other
limited resources of the wireless network. One of the
most important and challenging task of current and
future communication is transmission of high quality
image from source to destination with least error
where limitation of bandwidth is a prime problem [1].
By the advent of multimedia communication, the
multimedia transmission of multimedia over wireless
links is considered as one of the major application of
future communication systems, and such systems
require the use of high storage capacity and less error
transmission. Image processing includes any form of
information processing in which the input is an
image. Many image processing technique derive from
the application of signal processing techniques to the
domain of images 2-dimensional signals such as
photographs or video. Most of the signals processing
concepts that apply to one-dimensional signals such
as resolution, dynamic range, bandwidth, filtering etc.
are extend naturally to images as well [3-5]. Image
compression is an important field of research that has
been studied for nearly three decade. Compressed
images have numerous applications in diverse areas
such as high definition television, on-line product
catalogs and other multimedia application. Another
important application is browsing where focus is on
IJTSRD64684

International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
getting high compression. For many years, the most
popular image compression a technique was based on
the discrete cosine transform (DCT) [6-8]. In the
recent past, wavelets had emerged as an important
technique for image compression. The key idea
employed in image compression is that there is
statistical structure present in an image. Virtually all
image compression algorithms exploit this statistical
structure to devise a compressed representation of an
image. In recent years, many researchers have
proposed compression algorithms based on the
wavelet decomposition of an image. Since these
wavelet-based algorithms have proved to be very
successful [9].
A. Image Compression
In image compression the JPEG standard has already
been widely used. It uses DCT and Huffman coding
techniques. Its main disadvantage is when the coded
bit rate is lower than a certain value (about 0.25
bits/pixel), there are blocking effects in the decoded
image, due to the 88 block two-dimensional (2-D)
DCT [10-11]. Also, if the image is directly
transmitted over noisy a channel which is usually the
case for wireless applications it is easy to lose blocks,
because Huffman coding is a VLC. The noisier the
channel, the more blocks are lost. Recently the
wavelet decomposition has been proved to be a better
tool for image compression. Especially for high
compression ratios, it perform better than DCT based
JPEG. Thus, the new JPEG 2000 standard adopt
wavelet sub-band coding. Pixels that closed to each
other are called the neighborhood of the
representative pixel [12-15]. These related to 4-
neighbhor, 8-neighbhor,and n-neighbors
relationship.4-neighbors pixel are related to two
horizontal pixel and two vertically upward pixel.8-
neighbhor has two vertical, two horizontal,4-diagonal
pixel [12].
B. Need of Image Compression
In recent years, digital images are becoming more and
more important. Digital cameras are now cheap and
technically mature. As a consequence, digital images
are replacing conventional analog images in almost
every field. Example ranges from holiday pictures to
medical images, like x-ray tomography [13]. So, there
is a natural need to store image on a computer and
also to transmit them over the internet, to share them
with other persons. The big problem is that digital
images are quite memory-consuming, and so a need
to compress images is also quite natural if one wants
to store lots of images with a rather high resolution or
wants to transmit these images via a channel with
limited bandwidth [14]. Although memory is getting
cheaper and cheaper these days it is still not unlimited
and also the number and even more severe the
resolution of images one may want to store has
increased in the last years. Furthermore, we should
not forget that transferring images is still an issue, as
the bandwidth of networks, may they be wireless or
wired, is still quite limited, actually too limited to
transfer images in a raw format [13-16].
2. Daubechie Wavelet
These Daubechies wavelets are chosen to have the
highest number A of vanishing moments, means this
does not imply the good smoothness for given width
N=2A, and on the possible solutions that one is
chosen which scaling filter has external phase as
shown in Fig. 1. For fast wavelet transform is easy to
put into practice. These wavelets are mainly used for
solving self-similarity property of a signal. Haar and
Daubechies wavelet have orthogonality, & they have
some nice features [17-20]:
 Wavelet function and the scaling function are
same for forward and inverse transform.
 Different subspaces between the correlation in the
signal are removed. The Haar wavelet transform
is simplest type of wavelet, and fastest compare to
other wavelet. But because of its discontinuity, it
makes difficult to simulate a continuous signal, is
main drawback.
Fig. 1: Waveforms of Daubechies Wavelet
3. PROPOSED METHODOLOGY
Image de-noising is an active area of research in digital image processing. The aim of image de-noising is to
restore/recover original image from corrupted one with no or minimum distortion. The impulse noise is most

wide-spread and important noise in digital images. It affects image at the real time of acquisition due to noisy
sensor at the time of transmission due to channel errors (noise) or faulty memory locations in hardware by
synchronization errors in the image digitizing or transmission. The data that affected by salt-and-pepper noise
change drastically, because their amplitudes (amp.) are either relatively high or relatively low. If pixel values not
reflect the true intensities of the real scene, so it causes the degradation of the image quality. Various linear &
non-linear filtering scheme has been proposed for the removal of impulse noise. But linear filter lack usability
due to blurring of high-frequency (fh) components, and sharp details in the image. To overcome the shortcoming
of linear filters and non-linear filters have been adopted, and are still widely used for their useful properties like
edge preservation & robustness against impulse noise [17-18].
A. Quadrature Phase Shift Keying (QPSK)
This is also known as four-level PSK where each element represents more than one bit. Each symbol contains
two bits and it uses the phase shift of π/2, means 90º instead of shifting the phase 180º. In this mechanism, the
constellation consists of four points but the decision is always made in two bits. This mechanism can ensure the
efficient use of bandwidth and higher spectral efficiency. The principle equation (1) of QPSK Modulation of the
technique is [15]:
(1)
B. Fading Channels
Rayleigh and Rician fading channels are useful models of real-world phenomena in wireless communications.
These phenomena include multipath scattering effects, time dispersion, and Doppler shifts that arise from
relative motion between the transmitter and receiver.
The shaded shapes represent reflectors such as buildings. The major paths result in the arrival of delayed
versions of the signal at the receiver. In addition, the radio signal undergoes scattering on a local scale for each
major path. Such local scattering is typically characterized by a large number of Reflections by objects near the
mobile system. These irresolvable components combine at the receiver Rx.) & give rise to the phenomenon
known as multipath fading (e.g. MIMO). Each major path behaves as a discrete fading path [12-14].
C. Rayleigh Fading Channel
The information is transmitted in an environment with obstacles (Non Line-of-sight NLOS) as shown in Fig. 2,
more than one transmission paths will appear as result of the reflection(s). The receiver will then have to process
a signal which is a superposition of several different transmission paths. If there exists a large number of
transmission paths may be modeled as statistically independent; the central limit theorem will give the channel
the statistical characteristics of a Rayleigh Distribution [9].
Fig. 2: Non Line-of-sight prorogation
NLOS (indoor, city) Rayleigh fading occurs when there is no multipath LOS between transmitter and receiver
and have only indirect path which is called NLOS to receive the resultant waves. The Rayleigh Fading is one
kind of model which propagates the environment of radio signal. Rayleigh fading works as a reasonable model
when many objects in environment which scatter radio signal before arriving of receiver. When there is no

propagation dominant during line of sight between transmitter and receiver on that time Rayleigh Fading is most
applicable. On the other hand Rician Fading is more applicable then Rayleigh Fading when there is dominant
line of sight. During our simulation we used Rayleigh Fading when we simulate the performance of Bit Error
Rate (BER) verses Signal to Noise Ratio (SNR).
D. Rayleigh Fading Distribution
In mobile radio channels, the Rayleigh distribution is commonly used to describe the statistical time varying
nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. It
is well known that the envelope of the sum of two Quadrature Gaussian noise signals obeys a Rayleigh
distribution. The Rayleigh distribution has a probability density function (pdf) [18] given by:
P(r) = (2)
E. Compression Ratio (CR)
Compression ratio (CR) represents how much data is compressed using the compression algorithm with respect
to the original image size. So, this metric is an important measurement in image compressor’s performance
evaluation. Increase of CR is good for storage application since it reduces the transmission time consumption by
the image but at the same time it reduce the reconstructed image quality, so it is required between the
compression ratio and image quality metrics. In literature, several methods exist to measure the CR. For finding
Compression Ratio, we used number of bit to represent the size of original image and the number of bit to
represent the size compressed image. So, Compression ratio shows how much times image has been compressed.
By the ratio of the size of original data set to the size of the compressed data set we can find out compression
ratio.
(3)
Where X = Number of Bytes in the original data set, Y = Number of Bytes in the Compressed data set . It is
clearer by this example. Example: An image, 1024 pixel×1024 pixel×24 bit, without compression would require
3MB of storage. If after compression storage requirement is reduced to 300 KB, so by using formula we find the
compression ratio as 10:1.
4. Bit-Error-Rate (BER)
When number of bits error occurs within one second in a transmitted signal then we called it as Bit Error Rate
(BER). In another sentence Bit Error rate is one type of parameter which used to access the system that can
transmit digital signal from one end to other end. We can define BER as follows:
(4)
If transmitter and receiver’s medium are good in a particular time and Signal-to-Noise Ratio is high, then Bit
Error rate is low. In our thesis simulation we generated random signal when noise occurs after that we got the
value of Bit error rate.
5. Mean square error (MSE)
MSE is called squared error loss. These error measures the average of the square of the "error. It is incorporates
both the variance of the estimator and its bias so it is second moment of the error (about the origin). Mean square
error is minimizes the sum of squared errors due to bias and due to variance, so is criterion for an estimator. By
the average of the square of the difference between the desired response and the actual system output, MSE is
calculated. As a loss function, MSE is called squared error loss. For calculation, both the variance of the
estimator and its bias mentioned in equation 5.When estimator is unbiased, the MSE is the variance. Taking the
square root of MSE yields the root mean squared error or RMSE, by standard deviation which has the same units
as the quantity being estimated. For standard error, the RMSE is the square root of the variance, when estimator
is unbiased.
(5)
Where m and n is image size and I (i,j) is the input image and K (i,j) is retrieved image.

6. SNR (Signal-to-Noise Ratio)
Energy per bit to noise power spectral density ratio is important especially in simulation. Whenever we are
simulating and comparing the Bit Error rate (BER) the performance of adaptive modulation technique is very
necessary. The normalized form of is Signal-to-Noise Ratio (SNR). In tele-communication, Signal-to-Noise ratio
is the form of power ratio between a signal and background noise [20-21].
(7)
Here P is mean power. In this case the signal and the background noise are measuredwith the same point of view
if the measurement will take across the same impedance then SNR would be obtained by measuring the square
of the amplitude ratio.
(8)
In another word Signal to Noise Ratio: In many applications the Mean Square Error is
expressed in terms of a Signal to Noise Ratio (SNR) which defined in decibels (dB) as
(9)
Where is the variance of the desired image andis average variance.
7. Peak signal-to-noise ratio (PSNR)
The peak signal-to-noise ratio often abbreviated PSNR, is an term used for the ratio between the maximum
possible power of a signal and power of corrupting noise that affects the fidelity of its representation. So by the
ratio of signal variance and reconstruction error variance, PSNR can be defined[14].It is also explained as the
ratio between the maximum possible power of signal and the power of corrupting noise. Because many signals
have a very wide dynamic range, PSNR is usually expressed in terms of logarithmic decibel scale. So it is most
used as a measure of quality of reproduction of image compression etc. PSNR is easily defined which for two
monochrome images I and K where one of the images is considered noisy.
Encoding Time, Decoding Time and Transforming Time: Any compression system uses one of the encoding
techniques to encode the input information. The encoding operation is very crucial for the success of
compression system. It involves the representation of the input information in a form suitable for storage and
transmission. The time required to perform this operation is referred as encoding time. The reverse process to
encoding is decoding and the corresponding time required to decode an encoded data is decoding time. In
general, the information to be compressed will be represented in spatial domain. To compress the data, it was
observed that it is convenient to represent the data in frequency domain. Hence the information in time domain
needs to be converted into frequency domain. For that, one of the transforming techniques will be used. Again it
involves some time. This time is referred to as transforming time. These times are measured in seconds (s).
8. Simulation Result
The simulation result presented in the thesis focuses mainly on Compression ratio and PSNR which typically
affects the picture quality. Most of the times as researchers goes on increasing the compression ratio quality of
the resulting image use to go down for the proposed technique, test image “Cameraman.tif” size 256 *256. The
Results are shown in a quality measures such as SNR and BER for decompressed “Cameraman.tif” image are
calculated and compared. Table 1 shows the comparison of the results with the proposed technique of discrete
wavelet techniques Db2 wavelet with De-noising filter, Wiener filter and Median filter to the existing network
respectively.
9. Fading Channel on QPSK and 8-PSK Modulation with Db2 Transform
In this performance we consider flat fading channel on different modulation techniques with Db2 wavelet
transform. Most of the times as researchers go on increasing the compression ratio the quality of the resulting
image use to go down for the proposed technique, test image “Cameraman.tif” size 256 256.In the Fig. 3 (a)
show the (a) Original image, Compressed image and De-compressed image. The performance of Db2 Wavelet
transformer on QPSK modulation and 8-PSK modulation with Fading Channel as shown in Fig. 4 and Fig. 5
respectively.

origional image
50 100 150 200 250
50
100
150
200
250
Compressed image
20 40 60 80 100120
20
40
60
80
100
120
DeCompressed image
50 100 150 200 250
50
100
150
200
250
Fig. 3 (a) Original image, Compressed image and De-compressed image
0 2 4 6 8 10 12
10
-2
10
-1
10
0
BER vs SNR in flat fading
SNR
BER
Without filter
Wiener Filter
Median Filter
Fig 4: Performance of Db2 Wavelet Transformer on QPSK Modulation with Fading Channel
0 2 4 6 8 10 12
10
-2
10
-1
10
0
BER vs SNR in flat fading
SNR
BER
Witout Filter
Midian Filter
Wiener Filter
Fig 5: Performance of Db2 Wavelet Transformer on 8-PSK Modulation with Fading Channel
Table 1 Showing CR values on various stages
Wavelet Modulation Channel
CR
Without filter Wiener filter Median filter
Db2 QPSK Flat fading 7.3192 6.1780 8.4726
Db2 8-PSK Flat fading 7.0192 6.0195 8.3036
Table 2 PSNR values on various stages
Channel
model
PSK modulation
Wavelet
technique
PSNR
Without filter Wiener filter Median filter
Flat fading QPSK Db2 15.2458 15.6548 16.1604
Flat fading 8-PSK Db2 14.7627 14.8627 15.3723

Conclusion: This scenario underscores the critical
need for innovative compression techniques that not
only achieve high compression ratios but also
preserve image quality, especially in challenging
transmission environments. This approach aims to
provide a balanced solution that optimizes both
compression efficiency and image quality restoration
capabilities, even in the presence of channel
imperfections such as fading, thereby fulfilling the
pressing demands of modern digital imaging
applications. The performance output plotted between
BER verses SNR for QPSK and 8-PSK modulation
techniques with Channel (AWGN and Flat fading)
using Wiener filter and Median filter. From the
simulation results, we find that that if we increase
SNR value, BER performance is improved. We had
also noticed that if using Db2 wavelet compression
8.3726, increasing compression ratio for transmitting
image.
References:
[1] Wu, M. Wavelet Analysis for Image Denoising:
A Multiscale Approach for Enhancing Visual
Clarity. Preprints 2023, 2023101364.
https://doi.org/10.20944/preprints202310.1364.
v1
[2] Kim-Phung Truong Ming-Hung Shu Bi-Min
Hsu Thanh-Lam Nguyen, CASE IN
VIETNAM: WHAT FACTORS HAVE A
STRONG EFFECT ON GOLD PRICE IN 5
YEARS PERIOD , Global Journal of Advanced
Engineering Technologies and Sciences: Vol. 4
No. 4 (2017)
[3] Dipesh Gehlod Tarun kuril, PERMUTABLE
TECHNOLOGY , Global Journal of Advanced
No. 1 (2014)
[4] T. Guo, T. Zhang, E. Lim, M. López-Benítez,
F. Ma and L. Yu, "A Review of Wavelet
Analysis and Its Applications: Challenges and
Opportunities," in IEEE Access, vol. 10, pp.
58869-58903, 2022,
doi:10.1109/ACCESS.2022.3179517.
[5] H. Tekwani and K. Raj, "Compression using
Thresholding on Signal/Image by applying
Wavelet Analysis," 2018 International
Conference on Computational and
Characterization Techniques in Engineering &
Sciences (CCTES), Lucknow, India, 2018, pp.
17-20, doi:10.1109/CCTES.2018.8673979
[6] Ayse K. Arslan, RETHINKING
ROBUSTNESS IN MACHINE LEARNING:
USE OF GENERATIVE ADVERSARIAL
NETWORKS FOR ENHANCED
ROBUSTNESS. , Global Journal of Advanced
No. 2 (2022)
[7] R. Yadav, P. Moghe, M. Patidar, V. Jain, M.
Tembhurney and P. K. Patidar, "Performance
Analysis of Side Lobe Reduction for Smart
Antenna Systems Using Genetic Algorithms
(GA)," 2023 14th International Conference on
Computing Communication and Networking
Technologies (ICCCNT), Delhi, India, 2023,
pp. 1-5,
doi:10.1109/ICCCNT56998.2023.10306796.
[8] Meshach Owho Ojile, Elijah O. Ogwara,
VULNERABILITY OF COMMUNITIES TO
FLOOD HAZARD AND RIVERBANK
EROSION ALONG RIVER NUN IN
BAYELSA STATE, NIGERIA , Global Journal
of Advanced Engineering Technologies and
Sciences: Vol. 9 No. 3 (2022)
[9] Mansur Zakariyya Shuaibu Alhassan Bala,
WHATSAPP FORENSICS AND ITS
CHALLENGES FOR ANDROID
SMARTPHONE , Global Journal of Advanced
No. 5 (2016)
[10] Noureddine Aloui, Souha Bousselmi and
Adnane Cherif, "Optimized Speech
Compression Algorithm Based on Wavelets
Techniques and its Real Time Implementation
on DSP", I.J. Information Technology and
Computer Science, vol. 03, pp. 33-41, 2015.
[11] Shreyaskumar Patel "Optimizing Wiring
Harness Minimization through Integration of
Internet of Vehicles (IOV) and Internet of
Things (IoT) with ESP-32 Module: A
Schematic Circuit Approach", International
Journal of Science & Engineering Development
Research (www.ijrti.org), ISSN:2455-2631,
Vol.8, Issue 9, page no.95 - 103, September-
2023, Available:
http://www.ijrti.org/papers/IJRTI2309015.pdf
[12] M. Patidar, G. Bhardwaj, A. Jain, B. Pant, D.
Kumar Ray and S. Sharma, "An Empirical
Study and Simulation Analysis of the MAC
Layer Model Using the AWGN Channel on
WiMAX Technology," 2022 2nd International
Conference on Technological Advancements in
Computational Sciences (ICTACS), Tashkent,
Uzbekistan, 2022, pp. 658-662,
doi:10.1109/ICTACS56270.2022.9988033.
[13] Mike Meade, Shyamala C. Sivakumar and
William J. Phillips, "Comparative performance

of principal component analysis Gabor
wavelets and discrete wavelet transforms for
face recognition", Can. J. Elect. Comput. Eng.,
vol. 30, no. 2, Spring 2005.
[14] M. Patidar, R. Dubey, N. Kumar Jain and S.
Kulpariya, "Performance analysis of WiMAX
802.16e physical layer model," 2012 Ninth
International Conference on Wireless and
Optical Communications Networks (WOCN),
Indore, India, 2012, pp. 1-4,
doi:10.1109/WOCN.2012.6335540.
[15] P. Gupta, M. Patidar and P. Nema,
"Performance analysis of speech enhancement
using LMS, NLMS and UNANR algorithms,"
2015 International Conference on Computer,
Communication and Control (IC4), Indore,
India, 2015, pp. 1-5,
doi:10.1109/IC4.2015.7375561.
[16] Jacob Benesty, Shoji Makino, and Jingdong
Chen. 2006. Speech enhancement. Springer
Science & Business Media.
[17] Mikołaj Bi´nkowski, Jeff Donahue, Sander
Dieleman, Aidan Clark, Erich Elsen, Norman
Casagrande, Luis C Cobo, and Karen
Simonyan. 2019. High fidelity speech synthesis
with adversarial networks. In International
Conference on Learning Representations.
[18] Ingrid Daubechies. 1988. Orthonormal bases of
compactly upported wavelets. Communications
on pure and applied mathematics, 41(7):909–
996.
[19] Prafulla Dhariwal and Alexander Nichol. 2021.
Diffusion models beat gans on image synthesis.
Advances in neural information processing
systems, 34:8780–8794.
[20] Harishchandra Dubey, Ashkan Aazami, Vishak
Gopal, Babak Naderi, Sebastian Braun, Ross
Cutler, Hannes Gamper, Mehrsa Golestaneh,
and Robert Aichner. 2023. Icassp 2023 deep
noise suppression challenge. In ICASSP. James
L Flanagan. 2013. Speech analysis synthesis
and perception, volume 3. Springer Science &
Business Media.
[21] Florentin Guth, Simon Coste, Valentin De
Bortoli, and Stephane Mallat. 2022. Wavelet
score-based generative modeling. Advances in
Neural Information Processing Systems, 35:
478–491.

Enhancing Image Quality in Compression and Fading Channels A Wavelet Based Approach with Db2 and De noising Filters

More Related Content

Similar to Enhancing Image Quality in Compression and Fading Channels A Wavelet Based Approach with Db2 and De noising Filters

More from ijtsrd

Recently uploaded

Enhancing Image Quality in Compression and Fading Channels A Wavelet Based Approach with Db2 and De noising Filters