Using Quaternion Fourier Transform in Steganography Systems

steganography is the discipline of exchanging information messages in such way that no one, other than the intended recipient, suspects the existence of the message.  The transmitted message can be in textual or multimedia form (audio, image or video) and can be hidden within cover media. Moreover, the hidden message can be in either plain or cipher form.  In steganography, the majority of hiding techniques are implemented either in spatial domain or in frequency domain of the cover media.   The current contribution introduces a new a steganography technique for hiding a textual message within a cover image.   Both the message and the cover image is converted to quaternion form and then only the quaternion message is converted to the frequency domain using Quaternion Fast Fourier Discrete Transform (QFFDT) technique.  Simple quaternion mathematics are used to combine the message (in quaternion frequency domain) within the cover image (in quaternion form).  Conversely, the hidden message can be revealed at the receiver using simple quaternion mathematics in presence of the original cover image.  The proposed method allows hiding a huge amount of data and it is much complicated against steganalysis compared to the traditional methods. The method is assessed using the known performance metrics and the obtained results show that it is robust and more secure against steganalysis attacks without affecting the consumed bandwidth of the communication channel

The Applications of Discrete Wavelet Transform in Image Processing: A Review

This paper reviews the newly published works on applying waves to image processing depending on the analysis of multiple solutions. the wavelet transformation reviewed in detail including wavelet function, integrated wavelet transformation, discrete wavelet transformation, rapid wavelet transformation, DWT properties, and DWT advantages. After reviewing the basics of wavelet transformation theory, various applications of wavelet are reviewed and multi-solution analysis, including image compression, image reduction, image optimization, and image watermark. In addition, we present the concept and theory of quadruple waves for the future progress of wavelet transform applications and quadruple solubility applications. The aim of this paper is to provide a wide-ranging review of the survey found able on wavelet-based image processing applications approaches. It will be beneficial for scholars to execute effective image processing applications approaches

Color Image Analysis by Quaternion-Type Moments

International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

Elliptical Monogenic Wavelets for the analysis and processing of color images

International audienceThis paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filterbanks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize theanalytic signal representation for vector-valued signals. Then a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the article by defining the color local frequency, proposing an estimation algorithm