Regularization of Ill-Posed Problem
Regularization of Ill-Posed Point Neuron Models
... What are the practical consequences of our findings? As long as there does not exist very reliable biological information about the size of the steepness parameter β and the shape of the firing rate function S β , it ...
23
Expanding the applicability of Lavrentiev regularization methods for ill-posed problems
... the problem of approximating a solution of an ill-posed problem in a Hilbert space setting using the Lavrentiev regularization method and, in particular, expanding the applicability of ...
15
Regularization matrices for discrete ill-posed problems in several space-dimensions
... discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several ...very ill- conditioned and generally numerically singular, and the ...
20
A new highly anti-interference regularization method for ill-posed problems
... physics. Regularization methods can be applied to obtain the solution of ill-conditioned inverse problems by solving a family of neighboring well-posed ...the regularization methods to ...
6
A New Regularized Solution to Ill Posed Problem in Coordinate Transformation
... . Regularization is required to reduce the effects caused by the intrinsic ill-conditioning of the problem and noises in the data, and to stabilize the ...
7
Regularization of ill-posed inverse problem in ultrasound tomography
... 4.5 Regularization in UT with DSVD and DGSVD For the purpose of testing the regularization properties of the methods DSVD and DGSVD, we reconstructed a grayscale image of the Modi ed Shepp-Logan phantom as ...
125
An iterative regularization method for an abstract ill-posed biparabolic problem
... the problem of approximating a solution of an ill-posed biparabolic problem in the abstract ...original problem, we propose a regularizing strategy based on the Kozlov-Maz’ya iteration ...
17
Iterative regularization methods for ill-posed problems
... and ill-posed problems, a great deal of attention has been devoted to the regularization in the Banach space ...on regularization methods in Banach spaces was driven by different mathematical ...
272
Identification of source term for the ill posed Rayleigh–Stokes problem by Tikhonov regularization method
... source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative ...The problem is severely ill-posed in the sense of ...method ...
20
Lagrangian methods for the regularization of discrete ill-posed problems
... Tikhonov regularization, some strategies based on solving the quadratically constrained least squares problem ...pro- posed in the literature, the selection of a suitable regularization ...
60
Fractional regularization matrices for linear discrete ill-posed problems
... Tikhonov regularization allows the matrix A to be nonsymmetric or rect- ...Tikhonov regularization that m n; only minor modifications are required when m < ...Lavrentiev regularization can be ...
21
Regularization techniques based on Krylov subspace methods for ill-posed linear systems
... and regularization Inverse problems are ubiquitous in many areas of science and ...of regularization must be em- ...available problem with a related one having better numerical properties (in ...
156
Comparing Different Types of Approximators for Choosing the Parameters in the Regularization of Ill-Posed Problems
... Reynolds, Cross-referencing different regularized families of approximate solutions to ill-posed problems for solving the parameter choice problem in generalized CLS, [r] ...
12
Risk estimators for choosing regularization parameters in ill-posed problems - properties and limitations
... choose regularization parameters in ill-posed ...for ill-posed problems, since the properties in the data space do not tell much about the quality of the ...Tikhonov ...
38
Risk estimators for choosing regularization parameters in ill-posed problems - Properties and limitations
... choosing regularization parameters in ill-posed problems, in particular for sparsity ...for ill-posed problems, since the properties in the data space do not tell much about the quality ...
35
Convergence rates in regularization for a system of nonlinear ill posed equations with m accretive operators
... is ill-posed, because each one of the system is ...By ill-posedness, we mean that its solutions do not depend continuously on the data (A i , f i ...the regularization parameter choice without ...
9
Tikhonov-type iterative regularization methods for ill-posed inverse problems: theoretical aspects and applications
... The method proposed in Chapter 3 looks appealing for the problem describe above, however, it is difficult to apply in the physical setup we consider here. In fact, the norm of the noise, whose knowledge is ...
203
Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization
... inverse problem based on a linear operator with finite dimensional range is always well posed in the sense of Nashed [39], since the discrete forward operator has a closed ...an ill-posed PDE, ...
37
Solving Ill-posed Bilevel Programs
... suggested regularization techniques to implement well-posed bilevel optimization tech- niques in the framework of ill-posed ...the regularization parameter and function, ...lower-level ...
26
Ill-Posed and Linear Inverse Problems
... with ill- posed problems is that they are practically underdetermined due to the cluster of small singular values of ...the problem and to single out a useful and stable ...to regularization ...
8