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The classical Morrey spaces and Campanato spaces are generalized to the variable exponent case. The definitions and some basic properties of the variable exponent Morrey and Campanato spaces are presented. A concept of the p(⋅)-average of the functions is introduced.  相似文献   

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The concept of Feynman integral is considered in the sense of analytic continuation in the space of complex operators. The existence of the integral is proved and its representation in the form of a Gaussian integral is obtained for the case when the principal term of the integrand is an exponential of a polynomial.  相似文献   

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In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization problem leads to the generalized Sylvester matrix equation. For large-scale problems, we use the global-GMRES method which is an orthogonal projection method onto a matrix Krylov subspace. We present some theoretical results and give numerical tests in image restoration.  相似文献   

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The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic ${\overrightarrow{p}(x)}The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic p?(x){\overrightarrow{p}(x)} growth under suitable assumptions is proved. Based on this result, the global boundedness and the Lipschitz continuity of weak solutions of Dirichlet or Neumann boundary value problems for the p?(x){\overrightarrow{p}(x)}-Laplace type equations are obtained.  相似文献   

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In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.  相似文献   

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In this paper, we propose an efficient numerical scheme for solving some large‐scale ill‐posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited. First, the coefficient matrix is approximated as the sum of a small number of Kronecker products. This procedure not only introduces one more level of parallelism into the computation but also enables the usage of computationally intensive matrix–matrix multiplications in the subsequent optimization procedure. We then derive the corresponding Tikhonov regularized minimization model and extend the fast iterative shrinkage‐thresholding algorithm (FISTA) to solve the resulting optimization problem. Because the matrices appearing in the Kronecker product approximation are all structured matrices (Toeplitz, Hankel, etc.), we can further exploit their fast matrix–vector multiplication algorithms at each iteration. The proposed algorithm is thus called structured FISTA (sFISTA). In particular, we show that the approximation error introduced by sFISTA is well under control and sFISTA can reach the same image restoration accuracy level as FISTA. Finally, both the theoretical complexity analysis and some numerical results are provided to demonstrate the efficiency of sFISTA.  相似文献   

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A total variation model for image restoration is introduced. The model utilizes a spatially dependent regularization parameter in order to enhance image regions containing details while still sufficiently smoothing homogeneous features. A local variance estimator is used to automatically adjust the regularization parameter. A generalized hierarchical decomposition of the restored image is integrated to the algorithm in order to speed-up the performance of the update scheme. The corresponding subproblems are solved by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques. Numerical tests illustrate the performance of the algorithm. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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Alternating methods for image deblurring and denoising have recently received considerable attention. The simplest of these methods are two-way methods that restore contaminated images by alternating between deblurring and denoising. This paper describes Krylov subspace-based two-way alternating iterative methods that allow the application of regularization operators different from the identity in both the deblurring and the denoising steps. Numerical examples show that this can improve the quality of the computed restorations. The methods are particularly attractive when matrix-vector products with a discrete blurring operator and its transpose can be evaluated rapidly, but the structure of these operators does not allow inexpensive diagonalization.  相似文献   

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In the framework of the numerical solution of linear systems arising from image restoration, in this paper we present an adaptive approach based on the reordering of the image approximations obtained with the Arnoldi-Tikhonov method. The reordering results in a modified regularization operator, so that the corresponding regularization can be interpreted as problem dependent. Numerical experiments are presented.  相似文献   

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Wavelet-based multilevel approach is a promising method for image restoration problems. In this paper, a method for image restoration based on combining the symmlets family with two-level technique is proposed. A key feature is that the symmlets have many flexible attributes that lead to better stability and less artifacts. Computational experiments show that symmlets-based two-level method yields smaller relative errors and more stable results.  相似文献   

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We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators. Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.  相似文献   

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In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting (AOS) algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.  相似文献   

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In this work, a feasible direction method is proposed for computing the regularized solution of image restoration problems by simply using an estimate of the noise present on the data. The problem is formulated as an optimization problem with one quadratic constraint. The proposed method computes a feasible search direction by inexactly solving a trust region subproblem with the truncated Conjugate Gradient method of Steihaug. The trust region radius is adjusted to maintain feasibility and a line-search globalization strategy is employed. The global convergence of the method is proved. The results of image denoising and deblurring are presented in order to illustrate the effectiveness and efficiency of the proposed method.  相似文献   

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Robust priors for smoothing and image restoration   总被引:1,自引:0,他引:1  
The Bayesian method for restoring an image corrupted by added Gaussian noise uses a Gibbs prior for the unknown clean image. The potential of this Gibbs prior penalizes differences between adjacent grey levels. In this paper we discuss the choice of the form and the parameters of the penalizing potential in a particular example used previously by Ogata (1990,Ann. Inst. Statist. Math.,42, 403–433). In this example the clean image is piecewise constant, but the constant patches and the step sizes at edges are small compared with the noise variance. We find that contrary to results reported in Ogata (1990,Ann. Inst. Statist. Math.,42, 403–433) the Bayesian method performs well provided the potential increases more slowly than a quadratic one and the scale parameter of the potential is sufficiently small. Convex potentials with bounded derivatives perform not much worse than bounded potentials, but are computationally much simpler. For bounded potentials we use a variant of simulated annealing. For quadratic potentials data-driven choices of the smoothing parameter are reviewed and compared. For other potentials the smoothing parameter is determined by considering which deviations from a flat image we would like to smooth out and retain respectively.  相似文献   

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Approximation BFGS methods for nonlinear image restoration   总被引:1,自引:0,他引:1  
We consider the iterative solution of unconstrained minimization problems arising from nonlinear image restoration. Our approach is based on a novel generalized BFGS method for such large-scale image restoration minimization problems. The complexity per step of the method is of O(nlogn)O(nlogn) operations and only O(n)O(n) memory allocations are required, where nn is the number of image pixels. Based on the results given in [Carmine Di Fiore, Stefano Fanelli, Filomena Lepore, Paolo Zellini, Matrix algebras in quasi-Newton methods for unconstrained minimization, Numer. Math. 94 (2003) 479–500], we show that the method is globally convergent for our nonlinear image restoration problems. Experimental results are presented to illustrate the effectiveness of the proposed method.  相似文献   

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In this paper we present a convection-diffusion equation for processing image denoising, edge preservation and compression. We compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for Gaussian white noise. Here we show that this convection-diffusion model effectively removes noise, especially for the mixture of Gaussian and salt-and-pepper noises. We propose the modified streamline diffusion method [Y. Shih, H.C. Elman, Modified streamline diffusion schemes for convection-diffusion problems, Comput. Methods Appl. Mech. Eng, 1998.] for the discretization of this convection-diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression. Numerical experiments have shown that our convection-diffusion model for removing both Gaussian and salt-and-pepper noises, efficiently and reliably preserves edges quite satisfactorily.  相似文献   

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