heat equation and its comparative solutions in this paper we will conduct an analytic comparative study between the powerful adomian method and the traditional separation of variables method this is achieved by handling homogeneous and non homogeneous boundary value problem for one dimensional heat equation the study shows the reliability and efficiency of adomian method adomian method provides the solution in a rapidly convergent series through evaluating elegantly computable components

blur identification by the method of generalized cross validation the point spread function psf of a blurred image is often unknown a priori the blur must first be identified from the degraded image data before restoring the image generalized cross validation gcv is introduced to address the blur identification problem the gcv criterion identifies model parameters for the blur the image and the regularization parameter providing all the information necessary to restore the image experiments are presented which show that gvc is capable of yielding good identification results a comparison of the gcv criterion with maximum likelihood ml estimation shows the gcv often outperforms ml in identifying the blur and image model parameters

a note on optimal homotopy asymptotic method for the solutions of fractional order heat and wave like partial differential equations optimal homotopy asymptotic method oham is prolifically implemented to find the optimal solutions of fractional order heat and wave like equations we inspect the competence of the method by examining fractional order time dependent partial differential equations it is observed that oham is a prevailing and convergent method for the solutions of linear and nonlinear fractional order time dependent partial differential problems the numerical results rendering that the applied method is explicit effective and easy to use for handling more general fractional order heat and wave like models

new application of adomian decomposition method on fokker planck equation adomian decomposition method has been used for finding the explicit and numerical solutions of the reduced fokker planck equation in a force field the obtained results are compared with those found by other theories such as lie group theory the behaviour of the approximate distribution functions are shown graphically the results of lie group method confirm the correctness of those obtained by adomian decomposition method

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

filter design for mimo sampling and reconstruction we address the problem of finite impulse response fir filter design for uniform multiple input multiple output mimo sampling this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases the input signals are modeled as either continuous time or discrete time multiband input signals with different band structures we present conditions on the channel and the sampling rate that allow perfect inversion of the channel additionally we provide a stronger set of conditions under which the reconstruction filters can be chosen to have frequency responses that are continuous we also provide conditions for the existence of fir perfect reconstruction filters and when such do not exist we address the optimal approximation of the ideal filters using fir filters and a minmax l sub 2 end to end distortion criterion the design problem is then reduced to a standard semi infinite linear program an example design of fir reconstruction filters is given

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

multivariate mimo fir inverses the problem of computing exact finite impulse response fir inverses for multivariate multiple input multiple output mimo fir systems is considered necessary and sufficient conditions for invertibility are given along with computation techniques random systems and structured systems are defined necessary and sufficient conditions for the almost sure invertibility of structured random systems are derived bounds on the orders of the inverse filters are computed

on the solution of partial differential equations with specified boundary conditions abstract the decomposition method is applied to solution of partial differential equations in two and three dimensions with specified boundary conditions

vector sampling expansions in shift invariant subspaces multi input multi output mimo sampling scheme which is motivated by applications in multi channel deconvolution and multi source separation has been investigated in many aspects common for most of results on mimo systems is that the input signals are supposed to be band limited in this paper we study vector sampling expansions on general finitely generated shift invariant subspaces necessary and sufficient conditions for a vector sampling theorem to hold are given we also give several examples to illustrate the main result

sampling theorems for uniform and periodic nonuniform mimo sampling of multiband signals we examine a multiple input multiple output mimo sampling scheme for a linear time invariant continuous time mimo channel the input signals are modeled as multiband signals with different spectral supports and the channel outputs are sampled on either uniform or periodic nonuniform sampling sets with possibly different but commensurate intervals on the different outputs this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases we derive necessary and sufficient conditions on the channel and the sampling rate that allow stable perfect reconstruction of the inputs or equivalently perfect inversion of the channel from an implementation viewpoint we note that it is desirable that the reconstruction filters have continuous frequency responses we derive necessary and sufficient conditions that guarantee this continuity property the frequency responses of the reconstruction filters are specified as solutions to a system of linear equations finally we demonstrate that perfect reconstruction may be possible even when the channel outputs are sampled at an average rate that does not allow the reconstruction of any output from its samples alone in certain instances this average rate can achieve the recently presented fundamental bounds on mimo sampling density

multiple input multiple output sampling necessary density conditions we consider the problem of multiple input multiple output mimo sampling of multiband signals in this problem a set of input signals is passed through a mimo channel modeled as a known linear time invariant system the inputs are modeled as multiband signals whose spectral supports are sets of finite measure and the channel outputs are sampled on nonuniform sampling sets the aim is to reconstruct the inputs from the output samples this sampling scheme is quite general and it encompasses various others including papoulis generalized sampling and nonuniform sampling as special cases we introduce notions of joint upper and lower densities for collections of sampling sets and then derive necessary conditions on these densities for stable sampling and consistent reconstruction of the channel inputs from the sampled outputs these results generalize classical density results for stable sampling and interpolation due to landau

a variable coefficient korteweg de vries equation similarity analysis and exact solution ii a korteweg de vries kdv equation with time dependent coefficients is studied in this paper the similarity transformation for this system is investigated and an exact solution in a particular case is obtained the ablowitz ramani segur ars conjecture is used to identify the integrability of the system it is found that in some special cases the system may be integrable

solution of linear and nonlinear parabolic equations by the decomposition method adomian decomposition method adm has been applied to solve many differential equations in this paper we have used the adm to solve linear and nonlinear parabolic equation with variable parameters depends on time and space the adm does not need linearization or weak nonlinearity assumptions the results obtained indicate that the adm is efficient and accurate

multidimensional filter bank signal reconstruction from multichannel acquisition we study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup suppose that we have an channel convolution system referred to as analysis filters in dimensions instead of taking all the data and applying multichannel deconvolution we first reduce the collected data set by an integer uniform sampling matrix and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal first we determine the existence of perfect reconstruction pr systems for a given set of finite impulse response fir analysis filters second we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a fir pr synthesis polyphase matrix for a given set of fir analysis filters finally once a particular fir pr synthesis polyphase matrix is found we can characterize all fir pr synthesis matrices and then find an optimal one according to design criteria including robust reconstruction in the presence of noise

a generic effective nullstellensatz kollar s sharp effective nullstellensatz which is independent of the number of polynomials is shown to be a generically pessimistic bound a generic effective nullstellensatz is proven the generic bound is approximately inversely proportional to the number of polynomials further the bound is linear rather than exponential in the degrees of the polynomials the generic effective nullstellensatz provides for minimum required equalization filter orders in signal and image processing

variational iteration method with an auxiliary parameter for solving wave like and heat like equations in large domains abstract the present study is an attempt to obtain solutions of wave like and heat like equations with high dimensional in large domains through the well known variational iteration method vim which is coupled with an auxiliary parameter the convergence of the proposed method namely variational iteration method with an auxiliary parameter is under investigation in addition four examples are provided to elucidate the solution procedure and to optimally choose the auxiliary parameter comparing the results of the standard variational iteration method the auxiliary parameter proves very effective in controlling the convergence region of approximate solution

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

systems of convolution equations deconvolution shannon sampling and the wavelet and gabor transforms linear translation invariant systems e g sensors linear filters are modeled by the convolution equation s f mu where f is the input signal mu is the system impulse response function or more generally impulse response distribution and s is the output signal in many applications the output s is an inadequate approximation of f which motivates solving the convolution equation for f i e deconvolving f from mu if the function mu is time limited compactly supported and nonsingular it is proven that this deconvolution problem is ill posed a theory of solving such equations has been developed by berenstein et al it circumvents ill posedness by using a multichannel system if the signal f is overdetermined by using a system of convolution equations s i f mu i i 1 ldots n the problem of solving for f is well posed if the set of convolvers mu i satisfies the condition of being what is called strongly coprime in this case there exist compactly suppor

exact image deconvolution from multiple fir blurs we address the problem of restoring an image from its noisy convolutions with two or more blur functions channels deconvolution from multiple blurs is in general better conditioned than from a single blur and can be performed without regularization for moderate noise levels we characterize the problem of missing data at the image boundaries and show that perfect reconstruction is impossible even in the no noise case almost surely unless there are at least three channels conversely when there are at least three channels we show that perfect reconstruction is not only possible almost surely in the absence of noise but also that it can be accomplished by finite impulse response fir filtering such fir reconstruction is vastly more efficient computationally than the least squares solution and is suitable for low noise levels even in the high noise case the estimates obtained by fir filtering provide useful starting points for iterative least squares algorithms we present results on the minimum possible sizes of such deconvolver filters we derive expressions for the mean square errors in the fir reconstructions and show that performance comparable to that of the least squares reconstruction may be obtained with relatively small deconvolver filters finally we demonstrate the fir reconstruction on synthetic and real data

on incomplete lagrange function and saddle point optimality criteria in mathematical programming an incomplete lagrange function is used to study saddle point optimality criteria for a class of nonlinear programming problems under generalized convexity assumptions this study is further extended to certain class of fractional and generalized fractional programming problems as well

multidimensional multichannel fir deconvolution using grobner bases we present a new method for general multidimensional multichannel deconvolution with finite impulse response fir convolution and deconvolution filters using grobner bases previous work formulates the problem of multichannel fir deconvolution as the construction of a left inverse of the convolution matrix which is solved by numerical linear algebra however this approach requires the prior information of the support of deconvolution filters using algebraic geometry and grobner bases we find necessary and sufficient conditions for the existence of exact deconvolution fir filters and propose simple algorithms to find these deconvolution filters the main contribution of our work is to extend the previous grobner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general fir filters the proposed algorithms obtain a set of fir deconvolution filters with a small number of nonzero coefficients a desirable feature in the impulsive noise environment and do not require the prior information of the support moreover we provide a complete characterization of all exact deconvolution fir filters from which good fir deconvolution filters under the additive white noise environment are found simulation results show that our approaches achieve good results under different noise settings

a new look to multichannel blind image deconvolution the aim of this paper is to propose a new look to mbid examine some known approaches and provide a new mc method for restoring blurred and noisy images first the direct image restoration problem is briefly revisited then a new method based on inverse filtering for perfect image restoration in the noiseless case is proposed the noisy case is addressed by introducing a regularization term into the objective function in order to avoid noise amplification second the filter identification problem is considered in the mc context a new robust solution to the degradation matrix filter is then derived and used in conjunction with a total variation approach to restore the original image simulation results and performance evaluations using recent image quality metrics are provided to assess the effectiveness of the proposed methods

one phase inverse stefan problem solved by adomian decomposition method abstract in this paper the solution of one phase inverse stefan problem is presented the problem consists of the reconstruction of the function which describes the distribution of temperature on the boundary when the position of the moving interface is well known the proposed solution is based on the adomian decomposition method and the least square method

generic invertibility of multidimensional fir filter banks and mimo systems in this paper we study the invertibility of m variate laurent polynomial n times p matrices such matrices represent multidimensional systems in various settings such as filter banks multiple input multiple output systems and multirate systems given an n times p laurent polynomial matrix h z1 zm of degree at most k we want to find a p times n laurent polynomial left inverse matrix g z of h z such that g z h z j we provide computable conditions to test the invertibility and propose algorithms to find a particular inverse the main result of this paper is to prove that h z is generically invertible when n p ges m whereas when n p m then h z is generically noninvertible as a result we propose an algorithm to find a particular inverse of a laurent polynomial matrix that is faster than current algorithms known to us

least squares restoration of multichannel images multichannel restoration using both within and between channel deterministic information is considered a multichannel image is a set of image planes that exhibit cross plane similarity existing optimal restoration filters for single plane images yield suboptimal results when applied to multichannel images since between channel information is not utilized multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches a geometric interpretation of the estimates of both filters is given color images three channel imagery with red green and blue components are considered constraints that capture the within and between channel properties of color images are developed issues associated with the computation of the two estimates are addressed a spatially adaptive multichannel least squares filter that utilizes local within and between channel image properties is proposed experiments using color images are described

adomian decomposition method for solving fractional nonlinear differential equations in this article we have discussed a new application of adomian decomposition method on time fractional nonlinear fractional differential equations three models with fractional time derivative of order a 0 a 1 are considered and solved by means of adomian decomposition method the behaviour of adomian solutions and the effects of different values of a are investigated numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

revisited fisher s equation in a new outlook a fractional derivative approach abstract the well known fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system the modified model is analyzed both analytically and numerically a comparatively new technique residual power series method is used for finding approximate solutions of the modified fisher model a new technique combining sinc collocation and finite difference method is used for numerical study the abundance of the bird species phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters we conjecture non diffusive and diffusive fractional fisher equation represents the same dynamics in the interval memory index 0 8384 0 9986 we also observe that when the value of memory index is close to zero the solutions bifurcate and produce a wave like pattern we conclude that the survivability of the species increases for long range memory index these findings are similar to fisher observation and act in a similar fashion that advantageous genes do

exact solutions for heat like and wave like equations with variable coefficients in this paper adomian decomposition method is presented for solving heat like and wave like models with variable coefficients the method is demonstrated for a variety of problems in one and higher dimensional spaces where exact solutions are obtained the results obtained in all cases show the reliability and the efficiency of this method

fir perfect signal reconstruction from multiple convolutions minimum deconvolver orders given p co prime finite impulse response fir filters h sub i spl isin r m sub h it well known that there exist q sub i spl isin r m sub q such that spl sigma sub i h sub i q sub i spl delta importantly this enables signal recovery from its convolutions with p spl ges 2 co prime fir filters by fir filtering we show that such q sub i exist almost surely if and only if m sub q spl ges m sub h 1 p 1 where x is the smallest integer greater than or equal to x the results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem

numerical study of modified adomian s method applied to burgers equation the application of adomian s decomposition method to partial differential equations when the exact solution is not reached demands the use of truncated series but the solution s series may have small convergence radius and the truncated series may be inaccurate in many regions in order to enlarge the convergence domain of the truncated series pade approximants pas to the adomian s series solution have been tested and applied to partial and ordinary differential equations with good results in this paper pas both in x and t directions applied to the truncated series solution given by adomian s decomposition technique for burgers equation are tested numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution it is also shown in this paper that the application of adomian s method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences the so called method of lines may reduce the convergence domain of the solution s series

perfect blind restoration of images blurred by multiple filters theory and efficient algorithms we address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response fir filters we develop theoretical results about the existence and uniqueness of solutions and show that under some generically true assumptions both the filters and the image can be determined exactly in the absence of noise and stably estimated in its presence we present efficient algorithms to estimate the blur functions and their sizes these algorithms are of two types subspace based and likelihood based and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension we present memory and computation efficient techniques to handle the very large matrices arising in the two dimensional 2 d case once the blur functions are determined they are used in a multichannel deconvolution step to reconstruct the unknown image the theoretical and practical implications of edge effects and weakly exciting images are examined finally the algorithms are demonstrated on synthetic and real data

the decomposition method for initial value problems abstract in this paper initial value problems for the heat wave and plate equations in which the vectorial space variable varies in the whole r d will be handled using the reliable decomposition method the solutions are obtained in the form of rapidly convergent power series with elegantly computable terms showing that the new technique is reliable powerful and promising

on eigenstructure based direct multichannel blind image restoration existing eigenstructure based direct multichannel blind image restoration techniques include nullspace based and direct deconvolver estimation techniques the nullspace based approach can be formulated as an optimization problem we show that this formulation implies a new subspace based approach that uses matrix operations this new approach has the same advantages as the nullspace based one but requires less computational complexity under some mild conditions its complexity is equal to that of the fft furthermore the relation among the nullspace based approach the direct deconvolver estimation and the new subspace based approach is studied

multichannel blind deconvolution of spatially misaligned images existing multichannel blind restoration techniques assume perfect spatial alignment of channels correct estimation of blur size and are prone to noise we developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral this stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise we observe that the exact knowledge of the blur size is not necessary and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

he s homotopy perturbation method for continuous population models for single and interacting species he s homotopy perturbation method is applied for obtaining approximate analytical solutions of continuous population models for single and interacting species in comparison with existing techniques this method is very straightforward and the solution procedure is very simple also it is highly effective in terms of accuracy and rapid convergence analytical and numerical studies are presented

adomian decomposition method for solving the diffusion convection reaction equations abstract adomian decomposition method is used to solve the explicit and numerical solutions of three types of the diffusion convection reaction decr equations the calculations are carried out for three different types of the dcre such as the black scholes equation used in financial market option pricing fokker planck fp equation for lazer filed and fokker planck equation from plasma physics the behaviour of the approximate solutions of the distribution functions is shown graphically and compared with that obtained by other theories such as the variational iteration method

analytical approximate solution for fractional heat like and wave like equations with variable coefficients using the decomposition method abstract the time fractional heat like and wave like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order 0 2 the applications of the decomposition method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation some examples are presented to show the efficiency and simplicity of the method

a two step adomian decomposition method the adomian decomposition method adm is a nonnumerical method for solving a wide variety of functional equations and usually gets the solution in a series form in this paper we propose an efficient modification of adm namely two step adomian decomposition method tsadm that will facilitate the calculations we then conduct a comparative study between the tsadm and previous methods with the help of several illustrative examples the results obtained indicate that the tsadm is effective and promising

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences