63 research outputs found
Color Image Watermarking using JND Sampling Technique
This paper presents a color image watermarking scheme using Just Noticeable Difference (JND) Sampling Technique in spatial domain. The nonlinear JND Sampling technique is based on physiological capabilities and limitations of human vision. The quantization levels have been computed using the technique for each of the basic colors R, G and B respectively for sampling color images. A watermark is scaled to half JND image and is added to the JND sampled image at known spatial position. For transmission of the image over a channel, the watermarked image has been represented using Reduced Biquaternion (RB) numbers. The original image and the watermark are retrieved using the proposed algorithms. The detection and retrieval techniques presented in this paper have been quantitatively benchmarked with a few contemporary algorithms using MSE and PSNR. The proposed algorithms outperform most of them. Keywords: Color image watermarking, JND sampling, Reduced Biquaternion, Retrieva
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
Octonion special affine fourier transform: pitt's inequality and the uncertainty principles
The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transform, and other related transforms. This paper aims to introduce a novel octonion special affine Fourier transform (O-SAFT) and establish several classes of uncertainty inequalities for the proposed transform. We begin by studying the norm split and energy conservation properties of the proposed (O-SAFT). Afterwards, we generalize several uncertainty relations for the (O-SAFT) which include Pitt's inequality, Heisenberg-Weyl inequality, logarithmic uncertainty inequality, Hausdorff-Young inequality, and local uncertainty inequalities. Finally, we provide an illustrative example and some possible applications of the proposed transform
Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra
Low-rank approximation of images via singular value decomposition is
well-received in the era of big data. However, singular value decomposition
(SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a
higher order input into a matrix or break it into a series of order-two slices
to tackle higher order data such as multispectral images and videos with the
SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can
approximate higher order data using sums of a few rank-one components. We
consider the problem of generalizing HOSVD over a finite dimensional
commutative algebra. This algebra, referred to as a t-algebra, generalizes the
field of complex numbers. The elements of the algebra, called t-scalars, are
fix-sized arrays of complex numbers. One can generalize matrices and tensors
over t-scalars and then extend many canonical matrix and tensor algorithms,
including HOSVD, to obtain higher-performance versions. The generalization of
HOSVD is called THOSVD. Its performance of approximating multi-way data can be
further improved by an alternating algorithm. THOSVD also unifies a wide range
of principal component analysis algorithms. To exploit the potential of
generalized algorithms using t-scalars for approximating images, we use a pixel
neighborhood strategy to convert each pixel to "deeper-order" t-scalar.
Experiments on publicly available images show that the generalized algorithm
over t-scalars, namely THOSVD, compares favorably with its canonical
counterparts.Comment: 20 pages, several typos corrected, one appendix adde
Phase Retrieval of Quaternion Signal via Wirtinger Flow
The main aim of this paper is to study quaternion phase retrieval (QPR),
i.e., the recovery of quaternion signal from the magnitude of quaternion linear
measurements. We show that all -dimensional quaternion signals can be
reconstructed up to a global right quaternion phase factor from
phaseless measurements. We also develop the scalable algorithm quaternion
Wirtinger flow (QWF) for solving QPR, and establish its linear convergence
guarantee. Compared with the analysis of complex Wirtinger flow, a series of
different treatments are employed to overcome the difficulties of the
non-commutativity of quaternion multiplication. Moreover, we develop a variant
of QWF that can effectively utilize a pure quaternion priori (e.g., for color
images) by incorporating a quaternion phase factor estimate into QWF
iterations. The estimate can be computed efficiently as it amounts to finding a
singular vector of a real matrix. Motivated by the variants of
Wirtinger flow in prior work, we further propose quaternion truncated Wirtinger
flow (QTWF), quaternion truncated amplitude flow (QTAF) and their pure
quaternion versions. Experimental results on synthetic data and color images
are presented to validate our theoretical results. In particular, for pure
quaternion signal recovery, our quaternion method often succeeds with
measurements notably fewer than real methods based on monochromatic model or
concatenation model.Comment: 21 pages (paper+supplemental), 6 figure
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