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Bulletin of Electrical Engineering and Informatics
Vol. 12, No. 5, October 2023, pp. 2913~2922
ISSN: 2302-9285, DOI: 10.11591/eei.v12i5.5011 2913
Journal homepage: http://beei.org
Enhancement of DWT-SVD digital image watermarking against
noise attack using time–frequency representation
Mohanad Najm Abdulwahed, Ali Kamil Ahmed
Department of Materials Engineering, University of Technology, Baghdad, Iraq
Article Info
ABSTRACT
Article history:
Received Oct 14, 2022
Revised Dec 16, 2022
Accepted Feb 16, 2023
Information security has been defined as one of the most critical issues in the
information era, as it is utilized to protect confidential information during
transfers in real-world applications. In the case of image encryption, a
variety of information security approaches were used. Domain spatial and
domain frequency are two domains in which such techniques can be
classified. This study uses a combination of the singular value de-
composition (SVD) and discrete wavelet transformation (DWT) to construct
an encryption method based on a traditional watermarking system.
Compared with other traditional methods, the proposed DWT-SVD
approach has excellent robustness, and it has been strengthened for having
high degree of the robustness against the additive white Gaussian noise
(AWGN) attacks by utilizing a de-noising strategy based upon S-transform
approach. Compared with DWT algorithm denoising approach, the results
reveal that the S-transform denoising algorithm that has been deployed in the
present article has a robust protection towards the Gaussian noise attack for
mean squared error (MSE) around 0.005 and peak signal to noise ratio
(PSNR) around 24 dB.
Keywords:
Denoising
Encryption
Noise
Time-frequency
Wavelet
This is an open access article under the CC BY-SA license.
Corresponding Author:
Mohanad Najm Abdulwahed
Department of Materials Engineering, University of Technology
Baghdad, Iraq
Email: mohanad.najm97@gmail.com
1. INTRODUCTION
Image processing can be described as performing specific mathematical processes using signal
processing, with input being a picture, an image, video, image collection, or photo frame, and output being an
image or a collection of the image-related parameters or characteristics [1]. Many methods of image
processing include seeing images as 2-D signals and applying typical signal processing techniques. The
approaches of image encryption could be classified to 2 groups depending upon the operations of spatial and
frequency domains [2]. The former works in spatial domain, with encrypted artefacts such as pixel position
and intensity, whereas the latter works in frequency domain using the coefficients of frequency. The prior
encryption approaches work in the spatial domain. Approaches for spatial domain image encryption
necessitate a large number of the calculations [3]. Digital data is represented with regard to frequencies in the
transform domain. Various methods of digital watermarking in the transform domain have been published in
literature. Every approach in the transform domain has its own set of benefits and drawbacks. Discrete
wavelet transformation (DWT), discrete cosine transform (DCT), fast fourier transform (FFT), and discrete
fourier transform (DFT) are examples of different transforms utilized in the transform domain. The
watermark modifies coefficients of transform domain for inserting the watermark. Spread spectrum is
considered as the 3rd watermarking approach employed. Spread spectrum is a technique for spreading the
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energy of the watermark across visually relevant frequency bands so that the amount of the energy in any one
band is unnoticeable and small [4].
This work presents a DWT-singular value de-composition (DWT-SVD) based image encryption
approach depending on approaches of digital watermarking; results showed that the presented approach can
withstand almost all attacks; yet, the efficiency of the proposed scheme is unacceptably low when it comes to
Gaussian noise attacks. As a result, the research will focus on applying image denoising to improve
anti-attack capability against noise attacks with the use of S-transform. In the case when the signal of interest
has been damaged via noise, signal denoising is necessary to retrieve information that is carried by signal
with minimal error. De-noising approaches, like medial filtering [5], mean filter [6], variable digital filtering
[7], and Wiener filtering [8] have been indicated. Wavelet transform has lately gained popularity as a signal
de-noising approach [9], [10]. Adaptive wavelet shrinkage [11], wavelet correlation method [12], and
dual-tree complex wavelet coefficient are a few of the techniques presented [13].
2. DISCRETE WAVELET TRANSFORM
Regarding the operation of image processing, wavelets were used for watermarking, compression,
coding, sample edge detection, and de-noising of interesting characteristics in order to classify them
afterwards. Image denoising using thresholding DWT coefficients is discussed in the following sub-sections
[14]–[16]. DWT process and IDWT are discussed brifly in this section before the de-noising image process
begain against AWGN attacked.
2.1. Image data discrete wavelet transformation
Images are presented as two-dimensional array of the coefficients. The degree of the brightness
regarding each one of the points is represented by each coefficient. Almost all herbal images display smooth
coloring variations with excellent details that depict sharp edges from the simple versions. The clean color
changes could be referred to as versions of low-frequency, while pointy variations could be referred to as
versions of excessive-frequency. Furthermore, components of low-frequency (for example, smooth versions)
reveal image' base, whereas the components of excessive-frequency (such as, edges supplying details) were
uploaded onto components of low-frequency to refine an image, resulting in in-depth images. In addition, in
compared to the details, the easy versions have been considerable. Differentiating between simple variations
and photograph information can be done in a variety of ways. Image decomposition using DWT re-modeling
is an example of such a method. Figure 1 depicts different levels of decomposition in relation to DWT,
Figure 1(a) single-level, Figure 1(b) two-level and Figure 1(c) three-level decomposition.
(a)
(b)
(c)
Figure 1. Levels of DWT de-composition (a) single level decomposition, (b) two level decomposition, and
(c) three level decomposition [14]
2.2. Image’s inverse discrete wavelet transformation
The reverse wavelet transform was used to re-create an image from a variety of data classes. During
the process of re-construction, a pair of low-and high-pass filters were deployed as well. Synthesis filter pair
is the name given to the filters. The process of filtering is considered as the opposite of transformation; it
begins at the highest level. Filters were applied column-by-column first, then row-by-row until the lowest
level was reached.
3. SINGULAR VALUE DECOMPOSITION
The SVD method is a matrix transformation method that is based on eigenvalue. Every image could
be represented as matrix, which SVD might decompose to a summation of multiple matrices. While SVD
isn’t associated with frequency-to-spatial domain transformations, the singular image value has a high level
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of the stability; it is frequently combined with transformation techniques in image processing area. In a case
where the disturbances have been introduced to some image, the singular value is not significantly changed.
In addition, the singular vector of a matrix is invariant with regard to translation, rotation, and other
operations. As a result, singular value may be effectively reflecting matrix attributes. In a case of being
applied to an image's matrix, singular value, as well as its spanned vector space, may be reflecting numerous
image features and components. The algebraic features of an image may be described, and SVD was widely
used in image processing. Almost all current image encryption techniques are based on SVD, which has
increased robustness because of its stability and rotation invariance [17], [18].
A good method to compute eigenvalues and eigenvectors of data matrix X(K×M) was by using SVD
indicated in (1) [19]:
(1)
SVD theorem states that M×M matrix X can be de-composed into products of the following matrices:
(2)
where U is a K×K ortho-normal matrix containing left singular vectors which have been ordered column by
column:
(3)
V represent M×M orthonormal matrix associated with right singular vectors:
(4)
whereas represent K×M matrix with regard to non-negative real singular values:
(5)
Because of the features of SVD, certain watermarking computations have been proposed for this
system in the last two years. The main idea behind this method is finding SVD of the cover image and after
that alter its solitary properties to add a watermark. Because some of the SVD-based computations were
designated as SVD-situated, it's possible that lone SVD region was used for watermarking the image. Lately,
some half-and-half SVD-based computations have been suggested, where DWT, DCT, fast hadamard
transform, and other sorts of the changes space were employed so as to insert the watermark to an image [20].
4. S-TRANSFORM
S-transform represents a variant of short-time fourier transform (STFT), with frequency-dependent
Gauss window replacing window function. The width of a Gauss window is inversely proportionate to
frequency, whereas the height has been linearly scaled. S-transform has excellent time resolution for the
components of high-frequency and sufficient frequency resolution for the components of low-frequency due
to its window scaling behavior. The S-transform can be written as (6) [21]:
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(6)
where represent the signal and represent the frequency-dependent Gauss window, provided
by [21]:
(7)
The existence of variable f renders window spread frequency dependent. Taking under consideration
the fact that is complex valued, the modulus is typically plotted in practice for constructing a
representation of time–frequency. The local spectrum is represented by the S-transform; consequently,
averaging local spectrum throughout time yields fourier spectrum that is written as (8):
(8)
The signal in the representation of time is recoverable exactly from depending on the
next in [21], [22]:
(9)
Denoising is done in representation of time–frequency in this work, and the signal has been retrieved
from noise with (9). The discrete S-transform utilized in the present work to allow for the processing in
continuous S-transformation. Assuming that indicate discrete time series which
correspond to with an interval of time sampling of. S-transformation that is related to discrete time
series has been provided as (10):
(10)
The inverse discrete S-transformation is [23]:
(11)
5. STRATEGIES OF IMAGE DENOISING UTILIZING S-TRANSFORM
When it comes to the digital image processing, images are often under attacks by various noise
types, resulting in a reduction in image quality. Whether image noise is efficiently filter out or not, it will
impact consequent processing like the edge detection, image decryption, feature extraction, and object
segmentation. As illustrated in Figure 2, this work proposes a denoising approach depending upon analysis of
time–frequency employing S-transformation.
Figure 2. Flow graph of denoising process
The process of image denoising is described in the following phases: in (10) is used to apply a
discrete S-transform to a noisy image (image corrupted by additive white Gaussian noise (AWGN)).
S-transformation in (10) could be taken under consideration as convolution operation in frequency domain
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between signal X(k) and localizing scaled Gauss window (k), based on the principles of the DFT and
convolution theorem. S-transformation may be written as (12):
(12)
In the case where the image is regarded in the terms of the imaginary and real components, in (12)
may be represented as (13):
(13)
The exponential complex represented by (
) indicates the window shift in time-domain.
According to (13), frequency domain denoising process requires thresholding in the imaginary as well as the
real regions of spectrum. The value of the threshold is calculated as (14):
(14)
In which and respectively represent noise standard deviation for real and imaginary
parts. The kth noise standard deviation values can be estimated based on:
(15)
Following specifying threshold values for imaginary and real parts and the time-
frequency representations of imaginary and real parts after hard thresholding include:
(16)
After soft thresholding, the time-frequency representations of imaginary and real parts can be
represented as (17):
(17)
Combining imaginary and real parts yields the following time-frequency representation:
(18)
The inverse discrete S-transform could be used for recovering the denoised image x(n) in time
representation. Figure 3 shows the suggested denoising approach based upon S-transformation.
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Figure 3. Image denoising diagram
6. ENCRYPTION METHODS BASED ON THE DWT-SVD THROUGH THE UTILIZATION OF
THE METHODS OF DENOISING UTILIZING THE S-TRANSFORM
Utilizing de-noising methods before image decryption for increasing anti-attack capabilities
connected to this method against the noise attacks, based on the proposed DWT-SVD encryption methods
with usage of a normal image as the host image. In addition, in Figure 4, a new workflow was depicted.
Decryption and encryption processes could be given in the next method, according to Figure 4:
- Step 1: choosing original image and host image of the same size;
- Step 2: applying DWT to both images, as well as obtaining four sub-bands for each image, utilizing SVD
to each of subbands, and composing coincident subbands toward the original image and the host image;
and finally, application of the inverse-DWT to obtain encrypted-image, such a processing could be
referred to as DWT-SVD encryption technique;
- Step 3: denoising techniques utilizing the S-transform for filtering attacked the encrypted image during
transmission;
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- Step 4: the encrypted image will be decrypted, and the decryption process will be handled in the same
way as the encryption inverse operation; after that, the decrypted image will be obtained.
Figure 4. Suggested model
7. PERFORMANCE MEASURES
The normalized mean square error (NMSE), maximum absolute error (MAE), peak signal to noise
ratio (PSNR), and mean squared error (MSE) are some of the most used image reliability measurement
measures. SNR over 40 dB produces optimum image quality that is near to original image; signal to noise
ratio (SNR) 30-40 dB gives great quality of an image with appropriate distortions; SNR 20-30 dB produces
poor quality of an image; SNR less than 20 dB produces undesirable image [24]. In addition, the calculation
approaches for the PSNR and NMSE [25] were provided as (19):
(19)
where MSE represent MSE between the original image () and de-noised one () with an MxN size:
(20)
8. RESULTS AND DISCUSSION
We used two distinct techniques to watermark digital images, and each scheme yielded three
different result types, as shown in:
- Image watermarking/de-watermarking without any image attacks.
- Image watermarking/de-watermarking with Gauss noise image attack and denoising processing using
S-transform.
- Image watermarking/de-watermarking with Gauss noise image attack and denoising processing using
DWT.
MSE and PSNR are used to assess the quality of the recovered image. Due to slight errors in the image
extraction technique, a higher PSNR value indicates a higher quality of recovered image. MSE is a similarity
metric between two images that is close to zero. For illustrating the findings, we used the image buliding.
Figure 5 depicts the decrypted and encrypted image. The encrypted image is definitely identical to the host
image, depending on the results. In other words, the secret imag information had been efficiently hidden
inside the encrypted image. The details of the secret image are plainly visible in the decrypted images. We
discover that all four results fulfil our expectations, and the encryption approach depending on DWT-SVD
architecture performs admirably.
On the host image, the DWT-SVD noise method was used to watermark the original image. Then, a
Gauss image with variance-attacks was applied to water-mark image, after which the attack noise was
removed with the use of DWT technique. After that, it was dewatered, and obtained water-marked image is
shown in Figure 6.
On host image, DWT-SVD noise method was used to watermark the original image. Then, a Gauss
image with variance attack was applied to water-mark image, and after that the attack noise was removed
with the use of S-transform algorithm. After that, it was dewatered, and obtained water-marked image is
shown in Figure 7. Table 1 compares the performance of the suggested approach employing the S-transform
algorithm on noise power with a variance of 0.1 to the case without noise attack and the DWT-based
denoising approach. The noise power value is used for calculating the MSE and PSNR values.
Original
image DWT
transform
SVD
transform
in LH & HL
subbands
Encrypted
image
Image
attacked
with
Gaussian
noise
Denoising
using S-
transform
Image
decryption Decrypted
image
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Figure 5. Results for image encryption without noise attacks
Figure 6. Results of image encryption with Gauss noise attacks and decryption utilizing the DWT process
host image
original image
encrypted Image
decrypted image
host image
original image
encrypted Image
Gaussian noise encrypted image
decrypted image after denoising
decrypted image after denoising
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Figure 7. Results of image encryption with Gaussian noise attacks and decryption using S-transform
algorithm
Table 1. Comparison the performance of the suggested approach employing the S-transform algorithm with
another method
Cases
PSNR
MSE
No. attacks
212
0
DWT based on the daubechies wavelet biases
42.30
0.008
S-transform
66.121
0.0032
9. CONCLUSION
The findings of this work reveal that DWT-SVD based watermark method, along with S-transform
based de-noising algorithm, have provided the best efficiency in the presence of the recovery of the
watermark image which was attacked by Gauss noise. The results were evaluated analytically in terms of
PSNR and MSE, both of which were high for the new system of the DWT-SVD watermark. The MSE gives
an idea of how well the de-noised signal is similar to the original signal. A suitable criterion to compare the
performance of the various methods in de-noising the signals is to identify the technique that results in the
highest SNR with the lowest possible MSE.
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BIOGRAPHIES OF AUTHORS
Mohanad Najm Abdulwahed is an Associate Professor at the Department of
Materials Engineering, University of Technology Baghdad, Iraq, where he has been a faculty
member since 2013, mohand graduated B.Eng. degree in computer science from RUC
Baghdad, Iraq, an M.Sc. in Computer Science from Osmania University, Hyderabad India, as
well as a lecturer at Department of Materials Engineering, University of Technology Baghdad.
His research interests ar artificial intelligence, bioinformatics applications, image processing,
computer vision, and information security. He can be contacted at email:
mohanad.najm97@gmail.com.
Ali Kamil Ahmed was born in Baghdad, Iraq, in 1982. He received the B.Sc.
degree in computer technology engineering from Electrical Engineering Technical College-
Middle Technical University, and the M.Sc. degree in computer systems architecture from
Isfahan University of Technology, Iran. He is currently a Lecturer in Department of Materials
Engineering, University of Technology, Iraq. His current research interests include IoT,
wireless networks, artificial neural networks, and image processing. He can be contacted at
email: ali.k.ahmed@uotechnology.edu.iq.