full spectrum knowledge aware tensor model for energy resolved ct iterative reconstruction energy resolved computed tomography erct with a photon counting detector concurrently produces multiple ct images corresponding to different photon energy ranges it has the potential to generate energy dependent images with improved contrast to noise ratio and sufficient material specific information since the number of detected photons in one energy bin in erct is smaller than that in conventional energy integrating ct eict erct images are inherently more noisy than eict images which leads to increased noise and bias in the subsequent material estimation in this work we first deeply analyze the intrinsic tensor properties of two dimensional 2d erct images acquired in different energy bins and then present a f ull s pectrum knowledge aware tensor analysis and processing fstensor method for erct reconstruction to suppress noise induced artifacts to obtain high quality erct images and high accuracy material images the presented method is based on three considerations 1 2d erct images obtained in different energy bins can be treated as a 3 order tensor with three modes i e width height and energy bin and a rich global correlation exists among the three modes which can be characterized by tensor decomposition 2 there is a locally piecewise smooth property in the 3 order erct images and it can be captured by a tensor total variation regularization 3 the images from the full spectrum are much better than the erct images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance we then develop an alternating direction method of multipliers algorithm to numerically solve the presented fstensor method we further utilize a genetic algorithm to tackle the parameter selection in erct reconstruction instead of manually determining parameters simulation preclinical and synthesized clinical erct results demonstrate that the presented fstensor method leads to significant improvements over the filtered back projection robust principal component analysis tensor based dictionary learning and low rank tensor decomposition with spatial temporal total variation methods

the condition of vandermonde like matrices involving orthogonal polynomials the condition number relative to the frobenius norm of the n x n matrix p pi ltxj ly j l is investigated where p p dx are orthogonal polynomials with respect to some weight distribution dx and xi are pairwise distinct real numbers if the nodes x j are the zeros of p the condition number is either expressed or estimated from below and above in terms of the christoffel numbers for dh depending on whether the p are normalized or not for arbitrary real xi and normalized p a lower bound of the condition number is obtained in terms of the christoffel function evaluated at the nodes numerical results are given for minimizing the condition number as a function of the nodes for selected classical distributions dx

geometry of quasilinear hyperbolic systems with characteristic fields of constant multiplicity in this paper we study the regularity of the eigenvalues and eigenvectors and the existence of normalized coordinates for quasilinear hyperbolic systems with characteristic fields of constant multiplicity we prove that the eigenvalues and eigenvectors of the system have the same regularity as the coefficients of the system on the other hand we show that for the quasilinear hyperbolic system of conservation laws with characteristic fields of constant multiplicity the normalized coordinates exist on the domain under consideration

lower bounds for the condition number of a real confluent vandermonde matrix lower bounds on the condition numberp vc of a real con uent vander monde matrix vc are established in terms of the dimension n or n and the largest absolute value among all nodes that deflne the con uent vander monde matrix or n and the interval that contains the nodes in particular it is proved that for any modest kmax the largest number of equal nodes p vc behaves no smaller than on 1 p 2 n and than on 1 p 2 2n if all nodes are nonnegative it is not clear whether those bounds are asymp totically sharp for modest kmax

the condition number of real vandermonde krylov and positive definite hankel matrices we show that the euclidean condition number of any positive definite hankel matrix of order n geq 3 may be bounded from below by gamma n 1 16n with gamma exp 4 cdot it catalan pi approx 3 210 and that this bound may be improved at most by a factor 8 gamma n similar estimates are given for the class of real vandermonde matrices the class of row scaled real vandermonde matrices and the class of krylov matrices with hermitian argument improved bounds are derived for the case where the abscissae or eigenvalues are included in a given real interval our findings confirm that all such matrices including for instance the famous hilbert matrix are ill conditioned already for moderate order as application we describe implications of our results for the numerical condition of various tasks in numerical analysis such as polynomial and rational i nterpolation at real nodes determination of real roots of polynomials computation of coefficients of orthogonal polynomials or the iterative solution of linear systems of equations

shock reflection for a system of hyperbolic balance laws abstract this paper concerns shock reflection for a system of hyperbolic balance laws in one space dimension it is shown that the generalized nonlinear initial boundary riemann problem for a system of hyperbolic balance laws with nonlinear boundary conditions in the half space t x t 0 x 0 admits a unique global piecewise c 1 solution u u t x containing only shocks with small amplitude and this solution possesses a global structure similar to that of self similar solution u u x t of the corresponding homogeneous riemann problem if each characteristic field with positive velocity is genuinely nonlinear and the corresponding homogeneous riemann problem has only shocks but no centered rarefaction waves and contact discontinuities this result is also applied to shock reflection for the flow equations of a model class of fluids with viscosity induced by fading memory

singularity formation for the compressible euler equations with general pressure law abstract in this paper the singularity formation of classical solutions for the compressible euler equations with general pressure law is considered the gradient blow up of classical solutions is shown without any smallness assumption by delicate analysis of decoupled riccati type equations the proof also relies on a new estimate for the upper bound of the density

the mixed initial boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics in this paper we prove that the c0 boundedness of solution implies the global existence and uniqueness of c1 solution to the mixed initial boundary value problem for linearly degenerate reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the c0 norm of solution may blow up in a finite time this gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves the same result is still valid for the quasilinear hyperbolic system of rich type

the mixed initial boundary value problem for diagonalizable quasilinear hyperbolic systems in the first quadrant abstract in this paper we investigate the mixed initial boundary value problem for diagonalizable quasilinear hyperbolic systems with nonlinear boundary conditions on a half unbounded domain t x t 0 x 0 under the assumptions that system is strictly hyperbolic and linearly degenerate we obtain the global existence and uniqueness of c 1 solutions with the bounded l 1 l norm of the initial data as well as their derivatives and appropriate boundary condition based on the existence results of global classical solutions we also prove that when t tends to infinity the solutions approach a combination of c 1 travelling wave solutions under the appropriate assumptions of initial and boundary data the results can be applied to the equation of time like extremal surface in minkowski space r 1 1 n

discriminative feature representation to improve projection data inconsistency for low dose ct imaging in low dose computed tomography ldct imaging the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images to deal with this problem we propose here a new sinogram restoration approach the sinogram discriminative feature representation s dfr method different from other sinogram restoration methods the proposed method works through a 3 d representation based feature decomposition of the projected attenuation component and the noise component using a well designed composite dictionary containing atoms with discriminative features this method can be easily implemented with good robustness in parameter setting its comparison to other competing methods through experiments on simulated and real data demonstrated that the s dfr method offers a sound alternative in ldct

a d c optimization algorithm for solving the trust region subproblem this paper is devoted to difference of convex functions d c optimization d c duality local and global optimality conditions in d c programming the d c algorithm dca and its application to solving the trust region problem the dca is an iterative method that is quite different from well known related algorithms thanks to the particular structure of the trust region problem the dca is very simple requiring only matrix vector products and in practice converges to the global solution the inexpensive implicitly restarted lanczos method of sorensen is used to check the optimality of solutions provided by the dca when a nonglobal solution is found a simple numerical procedure is introduced both to find a feasible point having a smaller objective value and to restart the dca at this point it is shown that in the nonconvex case the dca converges to the global solution of the trust region problem using only matrix vector products and requiring at most 2m 2 restarts where m is the number of distinct negative eigenvalues of the coefficient matrix that defines the problem numerical simulations establish the robustness and efficiency of the dca compared to standard related methods especially for large scale problems

blow up of periodic solutions to linearly degenerate quasilinear hyperbolic systems an example is given to show that for the cauchy problem of n n homogeneous linearly degenerate quasilinear hyperbolic systems with periodic initial data when n 2 c1 solutions may blow up in a finite time no matter how small and smooth the initial data are

global existence of classical solutions to the mixed initial boundary value problem for quasilinear hyperbolic systems of diagonal form with large bv data abstract in this paper we investigate the mixed initial boundary value problem with large bv data for linearly degenerate quasilinear hyperbolic systems of diagonal form with general nonlinear boundary conditions in the half space t x t 0 x 0 as the result in a bressan contractive metrics for nonlinear hyperbolic systems indiana univ math j 37 1988 409 421 suggests that one may achieve global smoothness even if the c 1 norm of the initial data is large we prove that if the c 1 norm and the bv norm of the initial and boundary data are bounded but possibly large then the solution remains c 1 globally in time and possesses uniformly bounded total variation in x for all t 0 as an application we apply the result to the system describing the motion of relativistic closed strings in the minkowski space r 1 n

nonconvex splitting for regularized low rank sparse decomposition we develop new nonconvex approaches for matrix optimization problems involving sparsity the heart of the methods is a new nonconvex penalty function that is designed for efficient minimization by means of a generalized shrinkage operation we apply this approach to the decomposition of video into low rank and sparse components which is able to separate moving objects from the stationary background better than in the convex case in the case of noisy data we add a nonconvex regularization and apply a splitting approach to decompose the optimization problem into simple parallelizable components the nonconvex regularization ameliorates contrast loss thereby allowing stronger denoising without losing more signal to the residual

asymptotic behavior of classical solutions of reducible quasilinear hyperbolic systems with characteristic boundaries abstract in this paper we investigate the asymptotic behavior of classical solutions of reducible quasilinear hyperbolic systems with characteristic boundaries under some suitable assumptions we prove that the solution approaches a combination of lipschitz continuous and piecewise c 1 traveling wave solution as an application we apply the result to the equation for time like extremal surfaces in the minkowski space time r 1 1 n

blow up of solutions to the initial boundary value problem for quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal 66 1 2007 93 124 in the present paper we study the global structure instability of the self similar solution u u x t containing shocks contact discontinuities and at least one rarefaction wave of the initial boundary riemann problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 our result indicates that the kind of riemann solution u u x t mentioned above is globally structurally unstable as an application of our result we consider the model proposed by aw and rascle a aw m rascle resurrection of second order models of traffic flow siam j appl math 60 2000 916 938 describing traffic flow on a road network following the work of garavello and piccoli m garavello b piccoli traffic flow on a road network using the aw rascle model comm partial differential equations 31 2 2006 243 275 we prove the nonexistence of global piecewise c 1 solution containing one rarefaction wave of the initial boundary value problem for this model

shock free solutions of the compressible euler equations we study the structure of shock free solutions of the compressible euler equations with large data we describe conditions under which the rarefactive compressive character of solutions changes and conditions under which the vacuum is formed asymptotically we present several new examples of shock free solutions which demonstrate a large variety of behaviors

formation of singularities for certain hyperbolic systems in one space dimension we study the development of singularities of classical solutions of quasilinear strictly hyperbolic systems in one space dimension the systems are supposed to be in the diagonal form but we do not impose restrictions on the size of the initial data and in some cases we can replace the genuine nonlinearity by weaker conditions

sparse view spectral ct reconstruction using spectral patch based low rank penalty spectral computed tomography ct is a promising technique with the potential for improving lesion detection tissue characterization and material decomposition in this paper we are interested in kvp switching based spectral ct that alternates distinct kvp x ray transmissions during gantry rotation this system can acquire multiple x ray energy transmissions without additional radiation dose however only sparse views are generated for each spectral measurement and the spectra themselves are limited in number to address these limitations we propose a penalized maximum likelihood method using spectral patch based low rank penalty which exploits the self similarity of patches that are collected at the same position in spectral images the main advantage is that the relatively small number of materials within each patch allows us to employ the low rank penalty that is less sensitive to intensity changes while preserving edge directions in our optimization formulation the cost function consists of the poisson log likelihood for x ray transmission and the nonconvex patch based low rank penalty since the original cost function is difficult to minimize directly we propose an optimization method using separable quadratic surrogate and concave convex procedure algorithms for the log likelihood and penalty terms which results in an alternating minimization that provides a computational advantage because each subproblem can be solved independently we performed computer simulations and a real experiment using a kvp switching based spectral ct with sparse view measurements and compared the proposed method with conventional algorithms we confirmed that the proposed method improves spectral images both qualitatively and quantitatively furthermore our gpu implementation significantly reduces the computational cost

on the breakdown of solutions to n n quasilinear hyperbolic systems we shall be concerned with the development of singularities of the c1 solutions of the quasilinear n n hyperbolic system ut a u ux 0 in one space dimension generalizing a nonlinearity condition introduced by maccamy and mizel arch rat mech anal 25 1967 299 320 in this paper we prove some results of blow up for the first order derivatives without restrictions on the size of the initial data

how bad are hankel matrices considered are hankel vandermonde and krylov basis matrices it is proved that for any real positive definite hankel matrix of order n its spectral condition number is bounded from below by 3 cdot 2 n 6 also proved is that the spectral condition number of a krylov basis matrix is bounded from below by 3 frac 1 2 cdot 2 frac n 2 3 for v v x 1 ldots x n a vandermonde matrix with arbitrary but pairwise distinct nodes x 1 ldots x n we show that mbox rm cond 2 v geq 2 n 2 n frac 1 2 if either x j leq 1 or x j geq 1 for all j then mbox rm cond 2 v geq 2 n 2

global classical solutions to a kind of quasilinear hyperbolic systems in several space variables abstract for a kind of quasilinear hyperbolic systems in several space variables whose coefficient matrices commute each other by means of normalized coordinates formulas of wave decomposition and pointwise decay estimates the global existence of classical solution to the cauchy problem for small and decaying initial data is obtained under hypotheses of weak linear degeneracy and weakly strict hyperbolicity

analysis of singularities for one dimensional quasilinear hyperbolic systems using the method of new characteristic coordinates and the singularity theory of smooth mappings in this paper we analyze the long time behavior of smooth solutions for one dimensional quasilinear hyperbolic systems give a complete description of the solutions close to blow up points and provide some sharp estimates on the blow up rate of singularities

blow up mechanism of classical solutions to quasilinear hyperbolic systems abstract this paper deals with the blow up phenomenon of classical solutions to the cauchy problem for quasilinear hyperbolic systems with general small initial data which possess certain decaying properties we prove that it is the envelope of the same family of characteristics which yields the blowup of classical solutions to the cauchy problem moreover the blow up rate is also discussed

ticmr total image constrained material reconstruction via nonlocal total variation regularization for spectral ct this work develops a material reconstruction method for spectral ct namely total image constrained material reconstruction ticmr to maximize the utility of projection data in terms of both spectral information and high signal to noise ratio snr this is motivated by the following fact when viewed as a spectrally integrated measurement the projection data can be used to reconstruct a total image without spectral information which however has a relatively high snr when viewed as a spectrally resolved measurement the projection data can be utilized to reconstruct the material composition which however has a relatively low snr the material reconstruction synergizes material decomposition and image reconstruction i e the direct reconstruction of material compositions instead of a two step procedure that first reconstructs images and then decomposes images for material reconstruction with high snr we propose ticmr with nonlocal total variation nltv regularization that is first we reconstruct a total image using spectrally integrated measurement without spectral binning and build the nltv weights from this image that characterize nonlocal image features then the nltv weights are incorporated into a nltv based iterative material reconstruction scheme using spectrally binned projection data so that these weights serve as a high snr reference to regularize material reconstruction note that the nonlocal property of nltv is essential for material reconstruction since material compositions may have significant local intensity variations although their structural information is often similar in terms of solution algorithm ticmr is formulated as an iterative reconstruction method with the nltv regularization in which the nonlocal divergence is utilized based on the adjoint relationship the alternating direction method of multipliers is developed to solve this sparsity optimization problem the proposed ticmr method was validated using both simulated and experimental data in comparison with fbp and total variation based iterative method ticmr had improved image quality e g contrast to noise ratio and spatial resolution

perturbation bounds for polynomials using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly improve the results of ostrowski acta math 72 99 257 1940 elsner et al linear algebra appl 142 195 209 1990 a comparison of different perturbation bounds shows that our results are better in many cases than the similar local result of beauzamy can math bull 42 1 3 12 1999 using the matrix theoretical approach we also improve the backward stability result of edelman and murakami proceedings of the fifth siam conference on applied linear algebra siam philapdelphia 1994 math comput 64 210 763 1995

singularities of solutions for first order quasilinear hyperbolic systems in this paper the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the cauchy problem with essentially periodic small initial data or nonperiodic initial data a result of klainerman and majda is thus extended to the general case

the generalized nonlinear initial boundary riemann problem for quasilinear hyperbolic systems of conservation laws abstract in this paper we study the nonlinear initial boundary riemann problem and the generalized nonlinear initial boundary riemann problem for quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions on the domain t x t 0 x 0 under the assumption that each positive eigenvalue is either linearly degenerate or genuinely nonlinear we get the existence and uniqueness of the self similar solution to the nonlinear initial boundary riemann problem and of the global piecewise c 1 solution containing only shocks and or contact discontinuities to the corresponding generalized nonlinear initial boundary riemann problem it shows that the self similar solution to the nonlinear initial boundary riemann problem possesses the global structural stability

blow up of periodic solutions to reducible quasilinear hyperbolic systems under general assumption we prove that the smooth solution to reducible quasilinear hyperbolic system with periodic initial data in general develop singularities in finite time provided that the total variation on one period of the initial data is small

the concave convex procedure the concave convex procedure cccp is a way to construct discrete time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically this procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it in particular we prove that all expectation maximization algorithms and classes of legendre minimization and variational bounding algorithms can be reexpressed in terms of cccp we show that many existing neural network and mean field theory algorithms are also examples of cccp the generalized iterative scaling algorithm and sinkhorn s algorithm can also be expressed as cccp by changing variables cccp can be used both as a new way to understand and prove the convergence of existing optimization algorithms and as a procedure for generating new algorithms

global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields abstract in this paper we study the global existence and the asymptotic behavior of classical solution of the cauchy problem for quasilinear hyperbolic system with constant multiple and linearly degenerate characteristic fields we prove that the global c 1 solution exists uniquely if the bv norm of the initial data is sufficiently small based on the existence result on the global classical solution we show that when the time t tends to the infinity the solution approaches a combination of c 1 traveling wave solutions finally we give an application to the equation for time like extremal surfaces in the minkowski space time r 1 n

global existence of radial solutions for general semilinear hyperbolic systems in 3d abstract we study the well posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions we give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3d under null condition with small scaling invariant w 2 1 r 3 data we obtain a bilinear estimate that is effective for hyperbolic systems which do not have any time decay it allows us to achieve the boundedness of the weighted bv norm of the radial solutions

robust stability of lti systems over semialgebraic sets using sum of squares matrix polynomials this paper deals with the robust stability of discrete time linear time invariant systems with parametric uncertainties belonging to a semialgebraic set it is asserted that the robust stability of any system over any semialgebraic set satisfying a mild condition is equivalent to solvability of a semidefinite programming sdp problem which can be handled using the available software tools the particular case of a semialgebraic set associated with a polytope is then investigated and a computationally appealing method is proposed to attain the sdp problem by means of a sampling technique introduced recently in the literature furthermore it is shown that the current result encompasses the ones presented in some of the recent works the efficacy of the proposed method is demonstrated through some illustrative examples and the results are compared to some of the existing methods

cauchy problem for weakly linearly degenerate hyperbolic systems in diagonal form abstract we study the cauchy problem for quasi linear strictly hyperbolic systems of diagonal form with weakly linearly degenerate characteristics the global existence and uniqueness of c1 solution with initial data in c b 1 r w 1 1 r are proved when the l 1 r norm of or the c 0 r norm of is small we also give some examples to show that if the initial data are not in w 1 1 r or not small then the solution to the cauchy problem may blow up in a finite time

global structure stability of riemann solutions for general hyperbolic systems of conservation laws in the presence of a boundary abstract this work is a continuation of our previous work z q shao global structure instability of riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary j math anal appl 330 1 2007 511 540 in the present paper we study the global structure stability of the riemann solution u u x t containing only shocks and contact discontinuities of general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary we prove the existence and uniqueness of global piecewise c 1 solution containing only shocks and contact discontinuities to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws in the half space t x t 0 x 0 our result indicates that this kind of riemann solution u u x t mentioned above for general n n quasilinear hyperbolic systems of conservation laws in a half space possesses a global structural stability some applications to quasilinear hyperbolic systems of conservation laws arising in physics and other disciplines are also given

the global existence and the life span of smooth solutions to a class of complex conservation laws abstract in this paper we consider the cauchy problem for a class of complex conservation laws which is introduced by p d lax and essentially a class of quasilinear hyperbolic systems in two space dimensions for a kind of flux functions we prove the global existence of smooth solutions to the cauchy problem with small initial data on the other hand for different kinds of flux functions we give some estimates on the lower bound of the life span of smooth solutions

global existence of classical solutions to the cauchy problem on a semi bounded initial axis for a nonhomogeneous quasilinear hyperbolic system abstract it is proven that if the leftmost eigenvalue is weakly linearly degenerate then the cauchy problem for a class of nonhomogeneous quasilinear hyperbolic systems with small and decaying initial data given on a semi bounded axis admits a unique global c 1 solution on the domain t x t 0 x x n t where x x n t is the fastest forward characteristic emanating from the origin as an application of our result we prove the existence of global classical c 1 solutions of the flow equations of a model class of fluids with viscosity induced by fading memory with small smooth initial data given on a semi bounded axis

breakdown of classical solutions to the cauchy problem on a semi bounded initial axis for quasilinear hyperbolic systems abstract in this paper we consider the cauchy problem with initial data given on a semi bounded axis for quasilinear hyperbolic systems under the assumptions that the rightmost resp leftmost eigenvalue is not weakly linearly degenerate and the source term satisfies the corresponding matching condition we obtain a blow up result of a c 1 solution with small and decaying initial data

global solutions with shock waves to the generalized riemann problem for a system of hyperbolic conservation laws with linear damping abstract it is proven that a class of the generalized riemann problem for quasilinear hyperbolic systems of conservation laws with the uniform damping term admits a unique global piecewise c 1 solution u u t x containing only n shock waves with small amplitude on t 0 and this solution possesses a global structure similar to that of the similarity solution u u x t of the corresponding homogeneous riemann problem as an application of our result we prove the existence of global shock solutions piecewise continuous and piecewise smooth solution with shock discontinuities of the flow equations of a model class of fluids with viscosity induced by fading memory with a single jump initial data we also give an example to show that the uniform damping mechanism is not strong enough to prevent the formation of shock waves

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

global solutions with shock waves to the generalized riemann problem for a class of quasilinear hyperbolic systems of balance laws it is proven that the generalized riemann problem for a class of quasilinear hyperbolic systems of balance laws admits a unique global piecewise c1 solution u u t x containing only n shock waves with small amplitude on t 0 and this solution possesses a global structure similar to that of the similarity solution u u x t of the corresponding homogeneous riemann problem as an application of our result we prove the existence of global shock solutions piecewise continuous and piecewise smooth solution with shock discontinuities of the flow equations of a model class of fluids with viscosity induced by fading memory with a single jump initial data

norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils abstract we start by proving a lower bound for the lp operator norm of a submatrix with sufficiently large dimensions and some relations between the lp norm and the lp operator norm we then study the lp norm and the lp operator norm of certain matrices arising in estimating the eigenvalue generalized eigenvalue singular value and generalized singular value variations of matrices matrix pencils and matrix pairs finally as applications of our bounds upon the lp norm and lp operator norm of certain matrices we give several new bounds for the variations of the spectra of matrices and matrix pencils these new bounds are generalizations of the weyl lidskii theorem for hermitian matrices and the bhatia davis theorem for unitary matrices and of some results obtained by the author recently for diagonalizable pencils with real spectra

penalized likelihood pet image reconstruction using patch based edge preserving regularization iterative image reconstruction for positron emission tomography pet can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels the most commonly used quadratic penalty often oversmoothes edges and fine features in reconstructed images nonquadratic penalties can preserve edges but often introduce piece wise constant blocky artifacts and the results are also sensitive to the hyper parameter that controls the shape of the penalty function this paper presents a patch based regularization for iterative image reconstruction that uses neighborhood patches instead of individual pixels in computing the nonquadratic penalty the new regularization is more robust than the conventional pixel based regularization in differentiating sharp edges from random fluctuations due to noise an optimization transfer algorithm is developed for the penalized maximum likelihood estimation each iteration of the algorithm can be implemented in three simple steps an em like image update an image smoothing and a pixel by pixel image fusion computer simulations show that the proposed patch based regularization can achieve higher contrast recovery for small objects without increasing background variation compared with the quadratic regularization the reconstruction is also more robust to the hyper parameter than conventional pixel based nonquadratic regularizations the proposed regularization method has been applied to real 3 d pet data

global structure instability of riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal tma 66 1 2007 93 124 in this paper we study the global structure instability of the riemann solution u u x t containing shocks at least one rarefaction wave for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane our result indicates that this kind of riemann solution u u x t mentioned above for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given

shock reflection for general quasilinear hyperbolic systems of conservation laws abstract this paper concerns the reflection of shock waves for general quasilinear hyperbolic systems of conservation laws in one space dimension it is shown that the mixed initial boundary value problem for general quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions on the quarter plane t x t 0 x 0 admits a unique global piecewise c 1 solution u u t x containing only shock waves with small amplitude and this solution possesses a global structure similar to that of the riemann solution u u x t of the corresponding riemann problem if the positive eigenvalues are genuinely nonlinear and the riemann solution has only shock waves and no rarefaction waves and contact discontinuities our result indicates that the riemann solution u u x t consisting of only shock waves possesses a semi global nonlinear structure stability

tensor based dictionary learning for spectral ct reconstruction spectral computed tomography ct produces an energy discriminative attenuation map of an object extending a conventional image volume with a spectral dimension in spectral ct an image can be sparsely represented in each of multiple energy channels and are highly correlated among energy channels according to this characteristics we propose a tensor based dictionary learning method for spectral ct reconstruction in our method tensor patches are extracted from an image tensor which is reconstructed using the filtered backprojection fbp to form a training dataset with the candecomp parafac decomposition a tensor based dictionary is trained in which each atom is a rank one tensor then the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process and the alternating minimization scheme is adapted for optimization the effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets the results demonstrate that the proposed tensor based method generally produces superior image quality and leads to more accurate material decomposition than the currently popular popular methods

global classical solutions of mixed initial boundary value problem for quasilinear hyperbolic systems abstract in this paper we consider the mixed initial boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant t x t 0 x 0 under the assumptions that the system is strictly hyperbolic and linearly degenerate or weakly linearly degenerate the global existence and uniqueness of c 1 solutions are obtained for small initial and boundary data we also present two applications for physical models

initial boundary value problem for the equation of timelike extremal surfaces in minkowski space this paper investigate the mixed initial boundary value problem for the equation of timelike extremal surfaces in minkowski space r1 1 n in the first quadrant under the assumptions that the initial data are bounded and the boundary data are small we prove the global existence and uniqueness of the c2 solutions of the initial boundary value problem for this kind of equation based on the existence results on global classical solutions we also show that as t tends to infinity the first order derivatives of the solutions approach c1 traveling wave under the appropriate conditions on the initial and boundary data geometrically this means the extremal surface approaches a generalized cylinder which is an exact solution

mechanism of singularity formation for quasilinear hyperbolic systems with linearly degenerate characteristic fields abstract for the cauchy problem of 1 d first order quasilinear hyperbolic linearly degenerate systems a new mechanism of singularity formation is given to show that all the w 1 p 1 p norms of the c 1 solution should blow up simultaneously it gives a way to verify the property of ode singularity by directly using the energy method in the framework of c 1 solution

global existence of classical solutions to the cauchy problem on a semi bounded initial axis for quasilinear hyperbolic systems abstract in this paper we consider the cauchy problem with initial data given on a semi bounded axis for quasilinear hyperbolic systems under the assumption that the leftmost resp rightmost eigenvalue is weakly linearly degenerate we obtain the global existence and uniqueness of c 1 solution with small and decaying initial data

multi material decomposition using statistical image reconstruction for spectral ct spectral computed tomography ct provides information on material characterization and quantification because of its ability to separate different basis materials dual energy de ct provides two sets of measurements at two different source energies in principle two materials can be accurately decomposed from dect measurements however many clinical and industrial applications require three or more material images for triple material decomposition a third constraint such as volume conservation mass conservation or both is required to solve three sets of unknowns from two sets of measurements the recently proposed flexible image domain id multi material decomposition method assumes each pixel contains at most three materials out of several possible materials and decomposes a mixture pixel by pixel we propose a penalized likelihood pl method with edge preserving regularizers for each material to reconstruct multi material images using a similar constraint from sinogram data we develop an optimization transfer method with a series of pixel wise separable quadratic surrogate pwsqs functions to monotonically decrease the complicated pl cost function the pwsqs algorithm separates pixels to allow simultaneous update of all pixels but keeps the basis materials coupled to allow faster convergence rate than our previous proposed material and pixel wise sqs algorithms comparing with the id method using 2 d fan beam simulations the pl method greatly reduced noise streak and cross talk artifacts in the reconstructed basis component images and achieved much smaller root mean square errors

asymptotic behavior of global classical solutions to goursat problem of quasilinear hyperbolic systems abstract this work is concerned with the asymptotic behavior of global c 1 solutions of the goursat problem for quasilinear hyperbolic systems we prove that when t tends to the infinity the solutions approach a combination of c 1 traveling wave solutions at algebraic rate 1 t provided that the boundary data decay at the rate 1 t 1 where is a positive constant finally we give an application to the equation for motion of an elastic string

the mixed initial boundary value problem for quasilinear hyperbolic systems with linearly degenerate characteristics abstract in this paper we investigate the mixed initial boundary value problem with small bv data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space t x t 0 x 0 as the result in a bressan contractive metrics for nonlinear hyperbolic systems indiana univ math j 37 1988 409 421 suggests that one may achieve global smoothness even if the c 1 norm of the initial data is large we prove that if the c 1 norm of the initial and boundary data is bounded but possibly large and the bv norm of the initial and boundary data is sufficiently small then the solution remains c 1 globally in time applications to quasilinear hyperbolic systems arising in physics and mechanics particularly to the system describing the motion of the relativistic string in the minkowski space time r 1 n are also given

hyperbolic mean curvature flow in minkowski space abstract we study the hyperbolic mean curvature flow hmcf of graphs in minkowski space a quasilinear wave equation is derived and studied for the motion of smooth immersed spacelike acausal closed curves under hmcf based on this we investigate the formation of singularities in the motion of these curves some blow up results have been obtained and the estimates on the life span of the solutions are given furthermore our results show that the curvature of the limit curve become unbounded as t t max

global weakly discontinuous solutions for hyperbolic conservation laws in the presence of a boundary abstract this work is a continuation of our previous work in the present paper we study the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws with non linear boundary conditions in the half space t x t 0 x 0 under the assumption that each characteristic with positive velocity is linearly degenerate we prove the existence and uniqueness of global weakly discontinuous solution u u t x with small amplitude and this solution possesses a global structure similar to that of the self similar solution u u x t of the corresponding riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in physics and other disciplines particularly to the system describing the motion of the relativistic string in minkowski space r 1 n are also given

a note on the asymptotic behavior of global classical solutions of diagonalizable quasilinear hyperbolic systems abstract this paper is concerned with the asymptotic behavior of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields on the basis of the existence result for the global classical solution we prove that when t tends to the infinity the solution approaches a combination of c 1 traveling wave solutions provided that the c 1 norm and the bv norm of the initial data are bounded but possibly large in contrast to former results obtained by liu and zhou j liu y zhou asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems math methods appl sci 30 2007 479 500 ours do not require their assumption that the system is rich in the sense of serre applications include that to the one dimensional born infeld system arising in string theory and high energy physics