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Book ChapterDOI

A New SVD Based Watermarking Framework in Fractional Fourier Domain

TL;DR: The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks.
Abstract: In this paper, a new robust watermarking scheme is proposed using fractional Fourier transform (FrFT) and singular value decomposition. The core idea of the proposed scheme is to decompose an image using FrFT followed by the non-overlapping block segmentation. A new key matrix is then formed by taking maximum singular values of all non-overlapping blocks. For embedding this key matrix is used and is done by modifying singular values with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks.
Citations
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Journal ArticleDOI
TL;DR: A novel biometrically generated keys in the embedding process of a gray-scale watermark using a newly proposed mathematical transform, namely the fractional dual tree complex wavelet transform (FrDT-CWT), and singular value decomposition (SVD) are used.

67 citations

Journal ArticleDOI
TL;DR: The proposed fractional wavelet transform (FWT) image watermarking method is tested with different image processing attacks and under composite attacks to verify its robustness and security.
Abstract: This paper presents an efficient fractional wavelet transform (FWT) image watermarking technique based on combining the discrete wavelet transform (DWT) and the fractional Fourier transform (FRFT). In the proposed technique, the host image is wavelet transformed with two resolution levels, and then, the middle frequency sub-bands are FRFT transformed. The watermark is hidden by altering the selected FRFT coefficients of the middle frequency sub-bands of the 2-level DWT-transformed host image. Two pseudo-random noise (PN) sequences are used to modulate the selected FRFT coefficients with the watermark pixels, and inverse transforms are finally applied to get the watermarked image. In watermark extraction, we just need the same two PN sequences used in the embedding process and the watermark size. The correlation factor is used to determine whether the extracted pixel is one or zero. The proposed fractional wavelet transform (FWT) image watermarking method is tested with different image processing attacks and under composite attacks to verify its robustness. Experimental results demonstrated improved robustness and security.

26 citations


Cites methods from "A New SVD Based Watermarking Framew..."

  • ...The forward and inverse two-dimensional discrete fractional Fourier transform (2D-DFRFT) of an image is computed as [14]:...

    [...]

Journal ArticleDOI
TL;DR: The definition and implementation of redundant fractional wavelet transform is proposed followed by its use in watermark embedding and a reliable extraction process is developed for the extraction of both the watermarks from the possibly distorted image.

22 citations

Proceedings ArticleDOI
10 Apr 2012
TL;DR: The paper presents an efficient approach for digital image watermarking based on the Fractional Fourier Transform (FRFT), where a watermark in the form of a PN sequence is embedded in the coefficients of the FRFT implemented on the image in the spatial domain or in transform domain.
Abstract: The paper presents an efficient approach for digital image watermarking based on the Fractional Fourier Transform (FRFT). In this approach, a watermark in the form of a PN sequence is embedded in the coefficients of the FRFT implemented on the image in the spatial domain or in transform domain. The FRFT is used in this paper as a means of security. The objective of using other transform domains prior to the FRFT is to make use of the details in these transforms domains. Before extraction of the watermark image, we intentionally attack the watermarked image with different common image processing attacks to test the robustness of the proposed algorithms. The proposed Discrete Wavelet Transform Fractional Fourier Transform (DWT-FRFT) algorithm gives best robustness over the other algorithms under these attacks.

4 citations


Cites methods from "A New SVD Based Watermarking Framew..."

  • ...Two Dimensional Discrete Fractional Fourier Transform 2DFRFT: The forward and inverse two-dimensional discrete fractional Fourier transform (2D-DFRFT) of the image signal are computed as [13]:...

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  • ...A watermarking scheme based on the FRFT and Singular Value Decomposition (SVD) was presented in [13]....

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References
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Book
24 Oct 2001
TL;DR: Digital Watermarking covers the crucial research findings in the field and explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied.
Abstract: Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

2,849 citations


"A New SVD Based Watermarking Framew..." refers background in this paper

  • ...To ensure the rightful ownership and the authenticity of the original media, digital watermarking [1] is identified as a suitable solution....

    [...]

Book
01 Jan 1993
TL;DR: The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions as mentioned in this paper, including a new chapter on singular values and singular vectors, including ways to analyze a matrix of data.
Abstract: Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

1,913 citations


Additional excerpts

  • ...Few years ago, another transform called Singular Value Decomposition (SVD) [8,9] was explored for watermarking....

    [...]

  • ...Ganic presented hybrid-watermarking scheme based on DWT and SVD....

    [...]

  • ...After decomposing the cover image into four bands, SVD is applied on each band and modify the singular values of each band with the singular values of the visual watermark....

    [...]

  • ...SVD based scheme withstands a variety attacks but it is not resistant to geometric attacks like rotation, cropping etc....

    [...]

  • ...In this paper, a new robust watermarking scheme is proposed which is based on FrFT and SVD. Unlike existing SVD based watermarking scheme, proposed scheme embeds watermark in the singular values of the key matrix which is obtained from non-overlapping blocks segmentation, FrFT and SVD....

    [...]

Journal ArticleDOI
Victor Namias1
TL;DR: In this article, a generalized operational calculus is developed, paralleling the familiar one for the ordinary transform, which provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians.
Abstract: We introduce the concept of Fourier transforms of fractional order, the ordinary Fourier transform being a transform of order 1. The integral representation of this transform can be used to construct a table of fractional order Fourier transforms. A generalized operational calculus is developed, paralleling the familiar one for the ordinary transform. Its application provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians. The method of solution is first illustrated by its application to the free and to the forced quantum mechanical harmonic oscillator. The corresponding Green's functions are obtained in closed form. The new technique is then extended to three-dimensional problems and applied to the quantum mechanical description of the motion of electrons in a constant magnetic field. The stationary states, energy levels and the evolution of an initial wave packet are obtained by a systematic application of the rules of the generalized operational calculus. Finally, the method is applied to the second order partial differential equation with time-dependent coefficients describing the quantum mechanical dynamics of electrons in a time-varying magnetic field.

1,523 citations


"A New SVD Based Watermarking Framew..." refers background in this paper

  • ...1 Fractional Fourier Transform (FrFT) The concept of Fractional Fourier transform (FrFT) is introduced by Victor Namias in 1980 [15]....

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Journal ArticleDOI
TL;DR: A novel watermarking algorithm based on singular value decomposition (SVD) is proposed and results show that the newwatermarking method performs well in both security and robustness.
Abstract: Digital watermarking has been proposed as a solution to the problem of copyright protection of multimedia documents in networked environments. There are two important issues that watermarking algorithms need to address. First, watermarking schemes are required to provide trustworthy evidence for protecting rightful ownership. Second, good watermarking schemes should satisfy the requirement of robustness and resist distortions due to common image manipulations (such as filtering, compression, etc.). In this paper, we propose a novel watermarking algorithm based on singular value decomposition (SVD). Analysis and experimental results show that the new watermarking method performs well in both security and robustness.

978 citations


"A New SVD Based Watermarking Framew..." refers background in this paper

  • ...Few years ago, another transform called Singular Value Decomposition (SVD) [8,9] was explored for watermarking....

    [...]

  • ...Ganic presented hybrid-watermarking scheme based on DWT and SVD....

    [...]

  • ...After decomposing the cover image into four bands, SVD is applied on each band and modify the singular values of each band with the singular values of the visual watermark....

    [...]

  • ...SVD based scheme withstands a variety attacks but it is not resistant to geometric attacks like rotation, cropping etc....

    [...]

  • ...In this paper, a new robust watermarking scheme is proposed which is based on FrFT and SVD. Unlike existing SVD based watermarking scheme, proposed scheme embeds watermark in the singular values of the key matrix which is obtained from non-overlapping blocks segmentation, FrFT and SVD....

    [...]

Proceedings ArticleDOI
26 Oct 1997
TL;DR: A new multiresolution watermarking method based on the discrete wavelet transform (DWT), where Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image.
Abstract: We introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to often proposed methods to some common image distortions, such as the wavelet transform based image compression, and image halftoning. Moreover, the method is hierarchical. The computation load needed to detect the watermark depends on the noise level in an image.

441 citations


"A New SVD Based Watermarking Framew..." refers background in this paper

  • ...Embedding must be done either in spatial domain [2,7] or in frequency domain [4,5,6,7]....

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