two soft thresholding based iterative algorithms for image deblurring iterative regularization algorithms such as the conjugate gradient algorithm for least squares problems cgls and the modified residual norm steepest descent mrnsd algorithm are popular tools for solving large scale linear systems arising from image deblurring problems these algorithms however are hindered by a semi convergence behavior in that the quality of the computed solution first increases and then decreases in this paper in order to overcome the semi convergence behavior we propose two iterative algorithms based on soft thresholding for image deblurring problems one of them combines cgls with a denoising technique like soft thresholding at each iteration and another combines mrnsd with soft thresholding in a similar way we prove the convergence of mrnsd and soft thresholding based algorithm numerical results show that the proposed algorithms overcome the semi convergence behavior and the restoration results are slightly better than those of cgls and mrnsd with their optimal stopping iterations

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

concave cocirculations in a triangular grid let g be a planar digraph embedded in the plane such that each bounded face contains three edges and forms an equilateral triangle and let the union r of these faces be a convex polygon we consider the polyhedral cone b g formed by the real valued functions on the set of boundary edges of g with the following property there exists a concave function c on r which is affinely linear within each bounded face and satisfies c v c u e for each boundary edge e u v knutson tao and woodward obtained a result on honeycombs which implies that if the polygon r is a triangle then the cone b g is described by linear inequalities of horn s type with respect to so called puzzles along with obvious linear constraints the purpose of this paper is to give an alternative proof of that result working in terms of discrete concave functions rather than honeycombs our proof is based on a linear programming approach and a nonstandard flow model moreover the result is extended to an arbitrary convex polygon r as above

stability and hopf bifurcation of the stationary solutions to an epidemic model with cross diffusion in the previous paper cai and wang 2015 we investigated the stationary solutions of a cross diffusion epidemic model with vertical transmission in a spatially heterogeneous environment with neumann boundary condition and proved that the set of positive stationary solutions forms a bounded bifurcation branch which is monotone s or fish hook shaped with respect to the bifurcation parameter in the present paper we give some criteria on the stability of solutions on we prove that the stability of the solutions changes only at every turning point of while in a different case that a k and x are sufficiently large original stable positive stationary solutions at certain point may lose their stability and hopf bifurcation can occur these results are very different from those of the spatially homogeneous or without cross diffusion cases

namias fractional fourier transforms on l2 and applications to differential equations on considere les puissances fractionnaires de la transformee de fourier sur l espace l 2 et on donne des appplcations aux equations aux derivees partielles

transcale control for a class of discrete stochastic systems based on wavelet packet decomposition abstract in this paper a wavelet packet decomposition wpd based real time transcale linear quadratic gaussian lqg tracking control algorithm is given for a class of discrete stochastic systems which is developed with the state space models of wavelet packet coefficients at the coarsest scale decomposition layer established by haar wpd the wpd based transcale control algorithm provides a compromise between performance index and computational efficiency compared with the conventional lqg tracking control algorithm and it is an improvement of the wavelet transform based algorithm previously proposed simulation results are presented to demonstrate the effectiveness of the proposed algorithm

2d sine logistic modulation map for image encryption because of the excellent properties of unpredictability ergodicity and sensitivity to their parameters and initial values chaotic maps are widely used in security applications in this paper we introduce a new two dimensional sine logistic modulation map 2d slmm which is derived from the logistic and sine maps compared with existing chaotic maps it has the wider chaotic range better ergodicity hyperchaotic property and relatively low implementation cost to investigate its applications we propose a chaotic magic transform cmt to efficiently change the image pixel positions combining 2d slmm with cmt we further introduce a new image encryption algorithm simulation results and security analysis demonstrate that the proposed algorithm is able to protect images with low time complexity and a high security level as well as to resist various attacks

discrete fractional wavelet transform and its application to multiple encryption the fractional wavelet transform is a useful mathematical transformation that generalizes the most prominent tool in signal and image processing namely wavelet transform by rotation of signals in the time frequency plane the definition of discrete fractional wavelet transform is not reported yet in the literature therefore a definition of the discrete fractional wavelet transform is consolidated by discretizing continuous fractional wavelet transform in the proposed work possible applications of the transform are in transient signal processing image analysis image transmission biometrics image compression etc in this paper image transmission is chosen as the primary application and hence a novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel the proposed multiple image encryption scheme is consolidated by fractional wavelet transform and chaotic maps first all the images are encrypted followed by their sharing the sharing process is done considering numerical techniques by making the sharing process a system of linear equations experimental results and security analysis demonstrate the efficiency and robustness of the proposed primary application

image analysis by fractional order orthogonal moments orthogonal moments play an important role in image analysis and other similar applications however existing orthogonal moments are restricted to integer order and little investigation of non integer order orthogonal moments has been conducted to date in this paper a general framework of real order orthogonal moments also known as fractional order orthogonal moments is proposed in this general framework fractional order orthogonal moments can be defined in cartesian and polar coordinate systems shifted legendre polynomials are implemented in this paper to investigate the properties of fractional order orthogonal moments a series of experiments are performed which demonstrate that fractional order orthogonal moments are not only capable of region of interest roi feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition

a generalized fourier transform and convolution on time scales in this paper we develop some important fourier analysis tools in the context of time scales in particular we present a generalized fourier transform in this context as well as a critical inversion result this leads directly to a convolution for signals on two possibly distinct time scales as well as several natural classes of time scales which arise in this setting dilated closed under addition and additively idempotent we explore the properties of these time scales and demonstrate the utility of these concepts in discrete convolution mellin convolution and transformations of a random variable

continuous wavelet transform and continuous multiscale analysis abstract we study a generalization to the continuous wavelet transform of the concept of dyadic multiscale analysis useful in the analysis and application of orthonormal wavelet decompositions the resulting notion of scaling and its limitation is discussed and a possible modification is introduced with this modified notion of scaling the information loss which occurs when analyzing a signal with orthonormal wavelets i e using a discrete subset of the shift dilation plane only instead of performing the same analysis with continuously varying scale factors and translations is illustrated by analyzing an example signal

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

on localization properties of fourier transforms of hyperfunctions abstract in a g smirnov fourier transformation of sato s hyperfunctions adv math 196 2005 310 345 the author introduced a new generalized function space u r k which can be naturally interpreted as the fourier transform of the space of sato s hyperfunctions on r k it was shown that all gelfand shilov spaces s 0 r k 1 of analytic functionals are canonically embedded in u r k while the usual definition of support of a generalized function is inapplicable to elements of s 0 r k and u r k their localization properties can be consistently described using the concept of carrier cone introduced by soloviev m a soloviev towards a generalized distribution formalism for gauge quantum fields lett math phys 33 1995 49 59 m a soloviev an extension of distribution theory and of the paley wiener schwartz theorem related to quantum gauge theory comm math phys 184 1997 579 596 in this paper the relation between carrier cones of elements of s 0 r k and u r k is studied it is proved that an analytic functional u s 0 r k is carried by a cone k r k if and only if its canonical image in u r k is carried by k

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

a symmetric image encryption algorithm based on mixed linear nonlinear coupled map lattice abstract we propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear nonlinear coupled map lattices this spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does in the proposed image encryption we employ the strategy of bit level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

fourier transform and related integral transforms in superspace abstract in this paper extensions of the classical fourier fractional fourier and radon transforms to superspace are studied previously a fourier transform in superspace was already studied but with a different kernel in this work the fermionic part of the fourier kernel has a natural symplectic structure derived using a clifford analysis approach several basic properties of these three transforms are studied using suitable generalizations of the hermite polynomials to superspace see h de bie f sommen hermite and gegenbauer polynomials in superspace using clifford analysis j phys a 40 2007 10441 10456 an eigenfunction basis for the fourier transform is constructed

fast fourier transform using matrix decomposition to reduce both the multiplicative complexity and total number of operations this paper introduces a modeling scheme of the fast fourier transform fft to decompose the discrete fourier transform dft matrix recursively into a set of sparse matrices integrating three orthogonal transforms the hadamard modified haar and hybrid transforms the proposed scheme is able to obtain different fft representations with less computation operations than state of the arts to investigate the applications of the proposed fft scheme a multi stage image encryption algorithm is also introduced experimental results and security analysis are provided to show its encryption performance

hierarchy of chaotic maps with an invariant measure we give hierarchy of one parameter family x of maps at the interval 0 1 with an invariant measure using the measure we calculate kolmogorov sinai entropy or equivalently lyapunov characteristic exponent of these maps analytically where the results thus obtained have been approved with the numerical simulation in contrary to the usual one parameter family of maps such as logistic and tent maps these maps do not possess period doubling or period n tupling cascade bifurcation to chaos but they have single fixed point attractor for certain values of the parameter where they bifurcate directly to chaos without having period n tupling scenario exactly at those values of the parameter whose lyapunov characteristic exponent begins to be positive

positive steady states in an epidemic model with nonlinear incidence rate abstract in this paper we investigate a diffusive epidemic model with nonlinear incidence rate under homogeneous neumann boundary condition the value of this study lies in two aspects mathematically we show the stability of the constant positive steady state solution the existence and nonexistence the local and global structure of nonconstant positive steady states and epidemiologically we find that the system exhibits turing patterns controlled by diffusion

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed