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CHAPTER 4

STEGANOGRAPHY ALGORITHM BASED ON

DISCRETE WAVELET TRANSFORM FOR

ROBUSTNESS AND SECURITY

In this chapter, we address steganography algorithm based on discrete wavelet

transform for robust and secure. Firstly, the previous work on Wavelet transform

(WT) will be reviewed. Then a brief discussion of Fourier transforms comparison

with Discrete Wavelet Transform (DWT), in which a DWT is a useful in signals and

image processing. To reach the upper bound of satisfaction for Robustness and

security, an optimal DWT domain steganography algorithm is proposed. The

advantage of DWT over the previous algorithms introduced in our proposed

4.1 INTRODUCTION

Image processing is a rapidly growing area of computer science. It’s started

growing fast in various technological advances such as digital imaging, computer

processors and in many storage devices. In the novel digital era, digital

communication and digital image are playing crucial role and visual information has

tremendous impact on human lives. It becomes an inseparable part of our day-to-day

activities. The digital image is one of the media of information, especially in the field

of information hiding.

Digital image processing is concerned with inserting and extracting useful

information from images. For instance, hiding and retrieve the information from

images. Ideally, this is done by computers, with little or no human intervention.

STEGANOGRAPHY ALGORITHM BASED ON DISCRETE WAVELET TRANSFORM FOR ROBUSTNESS AND SECURITY

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“A picture is worth a thousand words.” In the modern era has introduced the standard

of digital information, especially in a digital image field associated with the benefits

and drawbacks.

The digital images in the field of steganography algorithm have a major difference

between spatial and frequency domain schemes is the convenience of implementation,

the two approaches can provide different functions to cope with various applications.

Generally, frequency or transform domains of steganography schemes tend to achieve

a better balance between robustness, security and fidelity than spatial domain.

Therefore, the embedded secret message procedures may have some image processing

technique. The image transforms coefficients; these coefficients have a large scale,

and perceptually important to the image representation. A large distortion on the

significant coefficients will result in serious quality degradation. Therefore,

embedding a secret message by slightly changing those significant coefficients will

result in a robust and secure steganography scheme because significant coefficients

usually remain stable even after image manipulation. The embedded of significant

coefficients can thus be detected more reliably. Therefore, the frequency domain

approaches are more popular in the steganography literature especially in DWT.

4.2 WAVELET TRANSFORM (WT)

The development of wavelets is a recently used in signal processing tool enabling

the analysis on several time scales of the local properties of complex signals that can

present non stationary zones [1-5].

A wave is a periodic oscillating disturbance that propagates through space and time,

usually with transference of energy. Wavelets are mathematical functions that divide

continuous time signal data into different frequency components.

A wavelet is a localized change of a sound signal in 1-D or localized variations of

detail in an image in 2-D.

The proliferations of wavelets are surprising in the scientific community,

academic as well as industrial. Wavelets lead to a massive number of applications in

various fields, such as geophysics, astrophysics, telecommunications, imagery and

information hiding, and a wide variety of signal processing tasks such as compression,

detecting edges, removing noise, and enhancing sound or images [6-12]. The

fundamental idea behind wavelets is to analyze according to scale.


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We use a process of scale to refine, understand and digest information. High scales

correlate with global information, and low scales correspond with the detailed

information. For instance, the large scale in image processing technique is the big

picture, while the small scale shows the details.

In the case of wavelets do not give the details about the time-frequency

representations, but gives details about the time-scale representations.

In various methods, the wavelet transform is similar to the Fourier transform. Where,

the wavelet transforms satisfy the mathematical measures to represent the input data

and uses the finite energy of the wavelet. However, the sinusoids to analyze signals

used by Fourier transform.

For every wavelet, there is a function ѱ called the mother wavelet described by

흍풋,풌(풙) = √ퟐ풋흍(ퟐ풋풙 − 풌),풋, 풌 = ퟎ,±ퟏ,… .. (4.1)

The mother wavelet recalls its name from the function she performs. She is the

prototype that generates the functions that are used in the wavelet transformation

process. She has children, grandchildren, great grandchildren, etc. She is only

constrained by the size of the original signal.

If the signal has 2n samples, she can give birth to n generations. For any mother ψ (x)

there is a function ϕ (x) called the scaling function (or sometimes called the father

wavelet). Its dilations are denoted by ϕ j, k. As the interval of the signal examined is

shifted, then the translation is the location of the interval, scale is the dilation [13, 14].

Various fields including mathematics, quantum physics, electrical engineering, and

seismic geology developed the concept of wavelets independently [15]. Therefore, it

is very difficult to credit everyone that has had an influence. Wavelets have been

outlined previously back to Alfred Haar in 1910 [16]. For many, the starting point of

their modern history coincides with two publications in the late 1980s by Ingrid

Daubechies [17, 18] and Stephane Mallat [19]. These innovators established a solid

mathematical foundation which would both explain and define the subject. Ingrid

Daubechies constructed the first orthogonal wavelet bases that were compactly

supported. Stephane Mallat is the father of Multiresolution analysis, which is the

foundation of contemporary wavelet philosophy. Mallat, a pioneer in the field,

established the idea that the wavelet transform, performed in a multi-scale manner, is

effective for analyzing the meaning of the content in images. A full background on


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wavelets and a theoretical treatment of wavelet analysis given by Daubechies can be

seen in [19, 20] for wavelet history.

The real-world applications based on wavelets have a multiple disciplines. This

application shows the perfect practical such as, Image Processing in JPEG 2000 [21]

image compression standards, the U.S. Federal Bureau of Investigation (FBI)

fingerprint compression standard [22]. Human Vision used in detecting filopodia

edges [23, 24], JPEG 2000 [21] image compression standards. Geophysics studies in

Tropical Convection [25], the El Nino Southern Oscillation (ENSO) [26, 27] and

Central England Temperature [28]. Ocean Engineering used for the Analysis of

Underwater Sonar [29], Tide Forecasting [30] and Ship Roll [31]. Astronomy and

Astrophysics defined the Tidal Tails around stellar systems [32], determination of

coronal plasma [33] and the solar cycle complexity [34]. Seismic Geology as used in

earthquake prediction [35].

The idea behind why the wavelet is particularly suited to analyze time-frequency

information for each of these applications. While, the Fourier transform is not fitting

for its need.

4.3 FOURIER TRANSFORM

Fourier Transform (FT) was established around since the early 1800s to represent

a signal in the frequency domain. Joseph Fourier is a French mathematician; has

defined the Fourier Transform as a periodic function that stated as an infinite sum of

periodic complex exponential functions. The FT reveals how much each frequency

contributes to the signal. In signal processing, the FT is defined with the equation:

푿(풇) = ∫ 풙(풕)풆 풊ퟐ흅풇풕풅풕 (4.2)

Where t denotes time, f denotes the frequency of X (f) describes the signal in the

frequency domain. X (t) denotes as a signal in the time domain. The axis and

amplitude are holding the frequency on a graph. -∞ to +∞ denotes as an integration

bounds. For the transformation equation, the left hand side of the transformation

equation, X (f) is a function of frequency, and the integration is over time. Therefore,

the integral is calculated for every value of f.

Discrete Fourier Transform (DFT) is used when the function of an analog required

operating on distinct and sampled values of a signal with finite periodic. The DFT

computes the X k from X n. The equation for the DFT is:


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푿풌 =ퟏ푵∑ 풙풏풆

ퟐ풙풊푵 풌풏풌 = ퟏ, ퟐ, …… .푵 − ퟏ푵 ퟏ

풏 ퟎ (4.3)

The DFT is a transform of finite-domain and discrete-time functions. Where, The Xk

denotes the amplitude and phase of the various components of the input signal xn. The

DFT’s values can be determined using a fast Fourier transform (FFT) algorithm. The

reverse process of FT is called as the inverse Fourier transforms, when a signal is

fixed into its constituent frequency elements, it can also be synthesized back into the

original signal.

푿(풇) = ∫ 풙(풕)풆풊ퟐ흅풇풕풅풕 (4.4)

The X (f), is the amplitude of the signal and phase, f (f), of the signal is demonstrated

in the superscript portion of e, if (f). The inverse DFT (IDFT) equation as:

푿풏 =ퟏ푵∑ 푿풌풆

ퟐ풙풊푵 풌풏풏 = ퟏ, ퟐ,…… . 푵 − ퟏ푵 ퟏ

풌 ퟎ (4.5)

The IDFT define the compute xn as a sum of components 푋 푒 with frequency

cycles per sample. The integration in the transformation equation is over time. The

left hand side is a function of frequency. Therefore, the integral is calculated for every

value of f.

FT can be a suitable tool to use if you are not interested in what times these frequency

components occur, but only interested in what frequency components exist.

There are many signals that are not stationary. An ECG (electrical activity of the

heart, electrocardiograph), an EEG (electrical activity of the brain,

electroencephalograph), and an EMG (electrical activity of the muscles,

electromyogram) are all examples of non-stationary signals. When the time

localization of the spectral component is needed, a transform giving the time-

frequency representation of the signal is needed. Wavelets do this and the short term

Fourier transform does this.

Short Term Fourier transform (STFT) is an FFT based method that provides time

and frequency localization to establish a local spectrum for any time instant. In the

STFT, the signal is divided into small enough segments, where these segments

(portions) of the signal can be assumed to be stationary.

Researchers approach has ended up with a revised version of the Fourier transform, as

short time Fourier transform (STFT). The equation follows:


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푺푻푭푻푿(흎)(풕 , 풇) = ∫풕[풙(풕)흎

∗(풕 − 풕′)]풆 풋ퟐ흅풇풕풅풕 (4.6)

The FT multiplied by a windowing function ω(t), t denotes as constrained to a time

period. X (t) denotes as the signal itself, ω (t) denotes as a window function, and *

denotes the complex conjugation. For every t and f a new STFT coefficient is

computed. In the STFT if the window is of finite length, there is no longer perfect

frequency resolution. So, there are various kinds of window uses in the STFT, We

require to have a short window in which the signal is stationary. The narrower we

make the window, the better the time resolution, and the better the assumption of

stationary, but the poorer the frequency resolution.

Wide windows give good frequency information, but poor time resolution, plus the

signal may not be stationary within the wide window. If a good window function is

chosen the STFT may be an excellent choice for an application.

A narrow window means good time resolution, but poor frequency resolution. A wide

window means good frequency resolution, but poor time resolution.

The usefulness of a mathematical function lies in its efficiency and versatility in

representing various types of signals in the physical world.

The Wavelet Comparison of Fourier, Where a Wavelet transforms have

advantages over traditional Fourier transforms for representing functions that have

discontinuities and sharp peaks, and for accurately deconstructing and reconstructing

finite, non-periodic and/or non-stationary signals.

This problem in the past decades several solutions, has been developed which are

more able to represent a signal in the time and frequency domain at the same time.

The representation of a function by wavelets, the wavelet transform, overcomes this

deficiency. The wavelet transform, at high frequencies, gives good time resolution and

poor frequency resolution, while at low frequencies, the wavelet transform gives a

good frequency resolution and poor time resolution. So, we can gather all of the

information for the analysis of the signal, and decide which pieces that are needed.

Linear algorithms are similarities between the FT and the WT, fast Fourier transform

(FFT) and the Discrete Wavelet Transform (DWT).

In the FFT, the basis functions are sines and cosines. Unlike the Fourier transform,

wavelet transforms do not have a unique set of basis functions. Rather, the set of

possible basis functions for the wavelet transform is infinite. These basis functions are

called wavelets, or mother wavelets.


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Wavelets are localized in space, while Fourier transforms are not. Wavelet

analysis communicates knowledge that time-frequency methods such as Fourier

analysis cannot. Fourier series basis functions, which last the entire interval, give

frequency information. The wavelet basis functions give frequency information, but

are local in time. Long basis functions give detailed j, k frequency analysis. Short

basis functions are suited for signal discontinuities. Short high-frequency basis

functions combined with long low-frequency give both. This all-inclusiveness is what

wavelet transforms naturally provide.

FT Gives us the global picture, no local information, the FT of most real life

signals are not combinations of sinusoids, FT is sufficient for stationary signal

analysis and linear time invariant (LTI) systems, FT has Poor performance when the

frequency changes with time, FT have not a compact support compared to WT, an

interval is compact if it contains both of its endpoints. For example, the interval, often

written using square brackets, is compact because it contains 0 and 1 [36].

Therefore, wavelets have their energy concentrated in time and are well suited for the

analysis of transient, time-varying signals. Transient signals have finite duration and

are any physical phenomena that are not stationary. Three examples in which the

human sensory system concentrates on the transients rather than the stationary are: a

syllable pronounced as part of a spoken sentence, an edge located in an image, and

abnormal electrocardiogram (ECG / EKG) pattern in a heartbeat. Since most of the

real-life signals encountered are time varying in nature, the Wavelet

Transform fits many applications very well [37].

4.4 WAVELET TRANSFORM (WT) AND MULTI SCALE FUNCTIONALITY

One of the most fundamental problems in signal processing is to find a suitable

representation of the data that will facilitate an analysis procedure. One way to

achieve this goal is to use transformation or decomposition of the signal on a set of

basis functions prior to processing in the transform domain. Transform theory has

played a key role in image processing for a number of years, and it continues to be a

topic of interest in theoretical as well as applied work. Image transforms are used

widely in many image processing fields, including image enhancement, restoration,

encoding, and description. Wavelet transforms and other multi-scale analysis


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functions have been used for compact signal and image representations in de- noising,

compression and feature detection processing problems for about twenty years. [35]

Multi scale is one of the most important features of wavelet transforms, [21], and

[35]. Physiological analogies have suggested that wavelet transforms is similar to low

level visual perception. From texture recognition, segmentation to image registration,

such multi-resolution analysis gives the possibility of investigating a particular

problem at various spatial-frequencies (scales). In many cases, a “coarse to fine”

procedure can be implemented to improve the computational efficiency and

robustness to data variations and noise. The transform coefficients had differing

statistics and perceptual importance. We use these differences to allocate bits for

encoding the different coefficients. This variable bit allocation resulted in a decrease

in the average number of bits required to encode the source output.

There are many mathematical transforms used to process the signal like FT

(Fourier Transform), STFT (Short Term Fourier Transform), DCT (Discrete Cosine

transform), Laplace Transform, Z Transform, Hilbert Transform and Wavelets etc.

[30, 31]. The theory of Wavelets starts with the concepts of Multiresolution Analysis

(MRA); the detailed theory of Multiresolution is found at [20, 21].

4.4.1 Continuous Wavelet Transform (CWT)

The Continuous Wavelet Transform was developed as an alternative approach to

overcome the resolution problem in the SFTF. A continuous wavelet transform is

used to divide a continuous-time function into wavelets. It is implemented in a similar

process as the SFTF: the signal is multiplied by a function, the mother wavelet instead

of a window function, and the transform is computed for individual portions of the

time-domain signal. However, the Fourier transform is not used and negative

frequencies are not computed, and the width of the window is modified for every

single piece of the spectrum. Diverse from the Fourier transform, the continuous

wavelet transform retains the way to construct a time-frequency, and make the

representation of a signal that proposals a good time and frequency localization.

The Continuous Wavelet Transform (CWT) is involution the sequence of input

data with a set of functions that generated through a mother wavelet. Usually, the

output of Xw (a, b) considers as a real valued function, but it is except when the

complex of mother wavelet is used. A complex mother wavelet method will transform


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the continuous wavelet transform of a complex valued function. The power spectrum

of the continuous wavelet transform can be denoted by |X w (a, b) |2, for instance, The

CWT has Haar and Morlet wavelet that used to analyze a square wave signal. The

analysis and the synthesis of the CWT is also extremely computer intensive

comparing to DWT that has been a simpler and more efficient implementation.

In the engineering and computer science field are commonly used the technique of

Discrete Wavelet Transform (DWT), and in the scientific research the technique of

Continuous Wavelet Transform (CWT) is mostly used. For the purpose of

steganography an image, we want a non-redundant representation of the image.

Additionally, the original and stego images must be the same size.

4.4.2 The Discrete Wavelet Transform (DWT)

The discrete wavelet transform (DWT) is in literature commonly associated with

signal expansion into (bi-) orthogonal wavelet bases. We shall adopt the same

convention in this thesis. Thus, as opposed to the highly redundant CWT, there is no

redundancy in the DWT of a signal; the scale is sampled at dyadic steps푎 ∈

2 : 푗 ∈ 푍 , and the position is sampled proportionally to the scale푎 ∈ 푘2 : (푗, 푘) ∈

푍 . By no means can a DWT be understood as a simple sampling By no means can a

DWT be understood as a simple sampling we are dealing with finite-energy signal

푓(푥) ∈ 퐿 (푅) the wavelet 휓(푥) has to be chosen such as {휓(2 (푥 − 2 푘))}( , )∈

of L2 the first such basis was constructed by Alfred Haar in 1909, and the choice for

better ones has culminated in Ingrid Daubechies’s work. The Haar basis is an

orthogonal, scale-varying basis and is the simplest of all wavelets. What is an

orthogonal, scale-varying basis? A basis function is a flexible mathematical

description of data distributed over space and time.

The systematic framework for constructing wavelet bases was known as the

Multiresolution analysis. In [38-41], provide a comprehensive treatment of these

topics. A particularly comprehensive filter bank point of view is [42, 43]. The

orthogonal wavelets are rarely available as closed form expressions, but rather

obtained through a computational procedure which uses discrete filters. The link

between wavelets and these discrete filters is essential for understanding the Mallat’s

fast DWT algorithm in the previous section and its extension to images.


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The DWT [44] provides a number of powerful image processing algorithms. The

operation of steganography techniques of DWTs have become more attractive to the

information hiding community [45, 46].

The Discrete Wavelet Transform has a long history of showing its appropriateness

for information hiding applications. The secret message can be embedded in the

higher level frequencies, which are not as perceptible to the human eye, by reaching

the wavelet coefficients in the HL and LH detail sub-bands. However, not much

attention has been given to which wavelet may be the most successful for the original

image used especially in the reassemble of the embedded secret messages.

For instance, the 1-D wavelet transform can be easily extended to 2-D. The 2-D data

or photographs, scatter plots and geographical measurements. In the 2-D case, the

operation is used in an input matrix instead of an input vector. To transform the input

matrix, we first apply the 1-D wavelet transform on each row. Then, take the resultant

matrix, and then apply the 1-D wavelet transform on each column. This gives us the

final transformed matrix. The 2-D wavelet transform is used extensively in image

compression. For a 2-D transform, the filter can along with the rows, making two sub-

images to create each half of the original size. The presence of the heights look

similar as the original, but the sub-images have half the width. Then, sub-images used

to filter a low and high-pass along with the columns, this generates two more sub-

images each, for a total of four sub-images called as decomposition or analysis. We

mention the resulting of sub-images from an iteration of the DWT called an octave as

LL (the approximation), LH (horizontal details), HL (vertical details), and HH

(diagonal details), to generate the sub-image of the filters.

4.4.3 Wavelet Decomposition and Reconstruction

The various ways to compute the wavelet transform can be achieved by reiterating

for the average and differentiate coefficients of a couple of filter bank [42, 43]. The

low pass and high pass filter, where each of the filters is expected to be sampled by

two. Therefore, each of those two output signals can be further transformed. In the

same way, the process can be frequent reiterate several times, the resulting in a tree

structure called the decomposition tree. The process of decomposition in wavelet

transform is aimed used to decompose signals and image process through wavelet [22,


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23]. Even the process of reconstruction is the reunited components back into the

original signal without loss of information.

In the figure shown below describe the Filter bank structure for one level

decomposition and reconstruction of two dimensional signals, and showing wavelet

decomposition at level 1, reconstruction, and four directions of image decomposition

and the decomposition of fruit image at 1-4 level.

Fig 4.1: Decomposition of wavelet at Level 1

Fig 4.2: Reconstruction of wavelet at Level 1

Fig 4.3: Representation Decomposition of fruits at level 1.


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Fig 4.4: Wavelet Decomposition at Level 1



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The main structure of Wavelet can be represented as a four channel perfect

reconstruction of the filter bank. The types of filter (HPF or LPF) indicating each

filter that is 2D with subscript for separation of horizontal and vertical components

[47, 48]. The outputs of four-transform components result are involved of all possible

mixtures of high and low pass filtering in the two directions. These filters can be used

in one stage of an image to decompose into four bands as shown in the figures above.

The detail of images for each resolution can be classified as Diagonal (HH), Vertical

(LH) and Horizontal (HL). The operations can be repeated on the low (LL) [33].


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4.4.4 Why the Discrete Wavelet Transform is needed?

The reason why the discrete wavelet transform is needed is depending according

to the application, applied to signals that based on mathematical transformations to

achieve additional data that is not available in the signal.

Wavelet transforms are used in a manner which divides a signal into those

components which are significant in time and space, and those that contribute less and

to be very useful in applications such as noise removal, edge detection and

information hiding.

In general, wavelets are useful when we try to obtain extra information from that

signal that is not available in the signal.

The signal transform is another method of representing the signal that will not modify

the information content available in the signal data.

Wavelets are contained of waves having energy focused on time or space, and it is

well suited for analyzing of transient signals. For instance, tide forecasting is

performed using wavelets. The ripples and trends in the ocean waters are transient,

and this is why wavelets were chosen.

The continuous wavelet transform (CWT) is a computation of the continuous

wavelet transform, where the wavelet series is the version used of the CWT. The

information used in it is offered the highly redundant to the extent that the

reconstruction of the signal is concerned. This type of redundancy needs a significant

of computation both time and resources. On the other hand, Discrete Wavelet

Transform (DWT) has abundant data from the original signal for both analysis and

synthesis, with an important reduction in the computation time. The DWT is easier

compare to CWT in the form of implementation.

For steganography, wavelets suitably and easily can break the image up into the

approximation and details. Wavelets will isolate and manipulated in high and low

resolution bandwidths, so that secret message can easily be embedded in the bands

which are less apparent to the human being eyes.

Multiresolution can analyze information embedded in an image with regards to time-

frequency content. It can be exploited to hide information in a way that humans will

not see. The information can be concealed in the details. The hidden information

should still remain robust because the approximation information is less likely to be

affected by image modification, such as compression or the addition of noise.


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Therefore, the wavelet transform has been successfully used to decompose complex

information and patterns into basic forms, having a track record and used several

other image processing applications.

4.4.5 Wavelet Domain for steganography Algorithms

The effective way to hide the secret data is depending on the choice of hiding

coefficients, i.e. on the transform domain used and the selection of the embedding

band. The steganography of wavelet transforms have been used in signal and image.

These include the global [49] and block based DCT [50], the DFT [51], the Fourier-

Mellin transform [52] and the fractal transform [53]. Other methods combine multiple

transforms. Some use the properties of the DFT and the DWT [54] while others utilize

the DCT and the DWT [55].

The steganography has an excellent description that is shown why wavelets are

well-suited for information hiding, especially on DWT [56].

The steganography approaches that use wavelets are classified in [56] as Algorithm

used to embed and extract the secret messages, Multiresolution strategy [57], Human

Visual System (HVS) modeling. The properties of the HVS are taken into account

either explicitly or implicitly, such as spatial masking, luminance masking and

contrast masking [58]. Other approaches use explicit perceptual measures called

contrast thresholds. Contrast thresholds, in general, refer to the minimum level of the

contrast that is observable by the human eye, Selection of the coefficients in the

embedding algorithm.

The best performance of wavelets in the information hiding is shown in [59, 60].

In [61] the embedding procedures in various images to obtain security and robustness,

even embed a secret message in the large coefficients of the high and middle

frequency details in wavelet by 2-level decomposition [62].

In [63] the system of embedding a 32-bit of the secret message in the image with

high redundancy, this idea of embedding is used to place one secret message at one

time in any iteration without repeating the same information.


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4.4.6 Advantages of DWT Steganography over the previous algorithms

Here some conditions why the DWT is suitable for steganography:

The DWT performs well for analyzing image features such as edges and

textures, especially in the space frequency localization.

Having the capability permits for the Embedder of secret message to reach to

the signal information when it may be used by other transforms, Such as

Multiresolution representation.

The wavelets transform used to break down an image into the approximation

HVS modeling for the robustness purpose.

The computational complexity of the DWT is O (n) used as Linear

complexity.

The wavelet transform is flexible and can be chosen according to the

properties of the image called as adaptively [66].

DWT has been existed to overcome the limitation of Short Time Fourier

Transform (STFT), which can be a useful for analyzing non-stationary signals.

The Wavelet Transform is useful when the multi-resolution technique

achieved by which the various frequencies are analyzed with different

resolutions.

It concentrated in time or space and suited to analysis of transient uses

wavelets of finite energy.

In Wavelet Transform, the sizes in the term of width that the function of

wavelet are changed with each spectral component.

Embedding is done by modifying least significant bits of selected wavelet

coefficients. Thus the number changeable coefficients in this case are equal to

the number of selectable coefficients.

It is an appropriate instrument for scrutinizing non-stationary signals that have

time varying spectra.

Wavelet transforms have advantages to cutouts and sharp peaks, and

analyzing, reconstructing finite, non-periodic and/or non-stationary signals.

It provides more information for analysis and synthesis, with an important

reduction in the computation time of the original signal and breaks the image

up into the approximation and details.


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4.5 STEGANOGRAPHY FOR ROBUSTNESS

The robust data hiding methods are also known as methods of the hidden data that

survive after various attacks. In this chapter, the data hiding term is referred for a

more general term including all hiding methods which can be robust or not. The

information hiding, especially in Steganography techniques has been studied in depth

than the non-robust techniques. These studies have been motivated by the emerging

needs of the combining text and image content providers which are looking for the

means to prevent the illegal distribution of their properties.

A passive adversary is the main difficulty that has evaded the steganography

solution that has multiplicity of the attacks. Such as random noise, friction or gravity;

but in the watermarking problem the adversary is a human being who can analyze the

system and better the attack strategy by time. The battle-of-wits situation between the

designer and the attacker for this problem puts the designer at a disadvantage because

of the multiplicity of attacks that needs to be accounted for. Steganography

researchers adopted some cryptographically techniques to discourage the attackers to

no avail. Some successful data hiding methods recover different attacks have been

proposed. The main ones of these methods are listed below:

Abdul-Jabbar et al. [64] in 2011, had worked with the effect of embedding domain

on the robustness in genetic watermarking proposed in frequency domain using

discrete wavelet transform (DWT), the robustness results for DWT are more than

DCT in the technique of watermarking that based on analyzing through Numerical

correlation. Th. Rupachandra et al. [65] in 2012, had given a proposed of an image

watermarking scheme based on visual cryptography in discrete wavelet transform that

practice various portions of a single watermark into various regions of the image. The

generate signals to be shared from the low frequency sub band of the original image

that's based on the binary watermark to study a global and local mean of DWT

technique. Manal and Thair [66] in 2011 proposed a technique that suggested

incorporating of double watermarks in a host image for improved protection and

robustness of wavelet domain in the second embedded data.

Chih-Chien et al. [67] in 2010, presents a novel of hiding secret text into the low

frequency of the overload component of a color image through the redundant discrete

wavelet transform. It gives a good result for imperceptibility and robustness. Po-Yueh

and Hung-Ju [68] in 2006, studies technique which embeds the secret messages in the


89

frequency domain where the algorithm is divided into two modes and 5 cases and

secret messages are embedded in the high frequency coefficients resulted from

Discrete Wavelet Transform. A. S. Imran et al. [69] in 2007, in their paper, discussion

a robust method that is encrypting the data and hide it that based on neighboring

pixels information” stated they can modify the Least Significant Bits technique for

data embedding by calculating the number bits that can be used for substitution based

on neighborhood pixel information.

Adaptive Methods are used in various from that a random embedding approach, it

adjusts the embedded signal to the local features of the original image. In [70] the

local characteristics of an image is first determined such as edge, uniform (non-edge)

with low/high intensity, moderately, very, extremely busy (high frequency terms).

The noise sensitivity of these classes is estimated and the signal is embedded

accordingly. In [71], the hidden signal is shaped to be masked by the original signal.

The computer simulations show that the throughput of the hiding system can be

improved with these techniques.

Invariance Methods are a novel approach to counter the expected attacks is to

insert the hidden signal into an invariant domain of the attack. If we desire the

invariancy to shifting, we can embed the hidden data to the amplitude of the Fourier

transform. The shift invariance idea is generalized to joint invariance under shift,

rotation and scaling in [72]. Due to the digitized nature of images, the domain

invariant to shift-scale-rotation operations turn out to be difficult to implement.

4.6 STEGANOGRAPHY FOR SECURITY

Privacy the indefeasible right of an individual to control the ways in which

personal information is obtained, processed, distributed, shared, and used by any other

entity" [73]. In addition, particular aspects of privacy lead to different but related

concepts, such as information privacy, communication privacy, bodily privacy, and

territorial privacy [74]. Anonymity technologies are more appropriate to guarantee

privacy [75]. Clearly, the items of interest in a steganographic system are the

messages themselves. Thus, steganography takes privacy in communications one step

further by making messages undetectable.

An ultimate goal in steganography is leading to both a secure steganographic

system and a private communication mechanism.


90

Sherin et al, [76] in 2011, discussed how to embed secret messages into grayscale and

RGB Colored images. They applied a wavelet domain method of third level

decompositions to determine the positions and the magnitudes to adaptively embed

the secret message steganography for concealing a huge amount of data with high

security, good invisibility. Saddaf and Younus [77] in 2012 had studied algorithm to

hide text in any colored images of any size using wavelet transform for the purpose of

improvement of image quality, security and imperceptibility. Jila et al. [78] in 2011

used gray scale images for discrete wavelet transform technique, where the chaotic

maps are employed to generate a key space with the length of 1040 numbers to

increase the amount of security. Furthermore, the XOR operator has been replaced by

the transformation process for embedding processing of the images. Chin-Chen et al.

[79] in 2005, presents a scheme for embedding secret data into a binary image that use

a serial number matrix in the place of a random binary matrix to reduce computation

cost and provide higher security protection on hidden secret data.

Our critical survey and While going through the literature of the steganography

enhancement based on discrete wavelet transform, the embedding of DWT may be

achieved by quantization scheme, where the coefficients of the host data are modified

according to the bit of secret message [80 - 83]. Spread spectrum signal, where the

algorithm of secret data can be embedded by a sequence of numbers usually

pseudorandom Gaussian sequence [84, 85], or image fusion, where the logo image is

used as a secret message instead of a pseudorandom sequence [86]. We identified the

following research issues in the existing schemes: Most of issues of discrete wavelet

transform, we surveyed, were developed to satisfy robustness of image from a various

attacks. Only a few numbers of researchers were working on combining text and

image for the different layers of security and robustness. However, this technique still

being produced in a various ways to perform better algorithm of security and

robustness by text, ciphertext, biometrics data that can be hidden in the host image as

our proposed scheme shown.


91

4.7 SUMMARY

An overview of the steganography algorithm based on discrete wavelet transform

with the purpose of robustness and security areas of interest. Hence it is focused in

this chapter the critical case study of Wavelet transform (WT), Fourier transforms,

Discrete Wavelet Transform (DWT), in which a DWT is a useful in signals and image

processing. It also reviewed the proposed of the Robustness and security, an optimal

DWT domain steganography algorithm. The survey of the approaches presented in the

literature to show the advantages of DWT over the previous algorithms are

introduced. Steganography enhancement based on combining text and image through

discrete wavelet transform will be described in our proposed approach in the next

chapter.

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