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1.
Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion
equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation
of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian
([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency
of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear
systems. We present computational results related to image processing and plane curve evolution.
Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001 相似文献
2.
Fiorella Sgallari 《Applied Mathematical Modelling》1985,9(4):295-301
A weak formulation for ‘direct’ boundary methods for time dependent parabolic problems, deduced from distribution theory, is presented. The present approach seems particularly valuable when dealing with problems with non-integrable singularities and solutions with an exponential growth. Numerical examples are also reported for plane diffusion. 相似文献
3.
Cascadic multilevel methods for the solution of linear discrete ill-posed problems with noise-reducing restriction and prolongation
operators recently have been developed for the restoration of blur- and noise-contaminated images. This is a particular ill-posed
problem. The multilevel methods were found to determine accurate restorations with fairly little computational work. This
paper describes noise-reducing multilevel methods for the solution of general linear discrete ill-posed problems. 相似文献
4.
The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side vector, which is contaminated by errors of unknown size. However, for large problems, the computation of the L-curve can be quite expensive, because the determination of a point on the L-curve requires that both the norm of the regularized approximate solution and the norm of the corresponding residual vector be available. Recently, an approximation of the L-curve, referred to as the L-ribbon, was introduced to address this difficulty. The present paper discusses how to organize the computation of the L-ribbon when the matrix of the linear system of equations has many more columns than rows. Numerical examples include an application to computerized tomography. 相似文献
5.
Elena 《高等学校计算数学学报(英文版)》2010,3(4)
<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets. 相似文献
6.
BIT Numerical Mathematics - This paper addresses the study of a class of variational models for the image restoration inverse problem. The main assumption is that the additive noise model and the... 相似文献
7.
Total variation regularization has good performance in noise removal and edge
preservation but lacks in texture restoration. Here we present a texture-preserving
strategy to restore images contaminated by blur and noise. According to a texture
detection strategy, we apply spatially adaptive fractional order diffusion. A fast
algorithm based on the half-quadratic technique is used to minimize the resulting
objective function. Numerical results show the effectiveness of our strategy. 相似文献
8.
Many questions in science and engineering give rise to linear discrete ill-posed problems. Often it is desirable that the computed approximate solution satisfies certain constraints, e.g., that some or all elements of the computed solution be nonnegative. This paper describes an iterative method of active set-type for the solution of large-scale problems of this kind. The method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time. 相似文献
9.
This paper presents an iterative method for the computation of approximate solutions of large linear discrete ill-posed problems by Lavrentiev regularization. The method exploits the connection between Lanczos tridiagonalization and Gauss quadrature to determine inexpensively computable lower and upper bounds for certain functionals. This approach to bound functionals was first described in a paper by Dahlquist, Eisenstat, and Golub. A suitable value of the regularization parameter is determined by a modification of the discrepancy principle. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65R30, 65R32, 65F10 相似文献
10.
Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since
the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed
problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating
knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete
ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate
that suitably chosen projections can enhance the accuracy of the computed solution. 相似文献