Analysis of bounded variation penalty methods for ill - posed problems
نویسنده
چکیده
This paper presents an abstract analysis of bounded variation (BY) methods for illposed apentor equations Au = L. Let where the penalty, or 'regularization'. parameter (I > 0 and the functional J ( u ) is the BY norm or semi-norm of U , also known 3s the total variation of U. Under mild restrictions on the operator A and the functional J ( u ) , it is shown that the functional T ( u ) has a unique minimizer which is stable with respen to certain perturbations in the data i, the operator A, the panmeter a, and the functional J ( u ) . In addition. convergence results are obtained which apply when these perturbations vanish and the regularization parameter is chosen appropriately. T ( u ) ~ I I A u r I l * + a r J ( u )
منابع مشابه
Analysis of Bounded Variation Penalty Methodsfor Ill - Posed
This paper presents an abstract analysis of bounded variation (BV) methods for ill-posed operator equations Au = z. Let T(u) def = kAu ? zk 2 + J(u); where the penalty, or \regularization", parameter > 0 and the functional J(u) is the BV norm or seminorm of u, also known as the total variation of u. Under mild restrictions on the operator A and the functional J(u), it is shown that the function...
متن کاملInverse Problems with Second-order Total Generalized Variation Constraints
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations [2]. It can be interpreted as a “sparse” penalization of optimal balancing from the first up to the kth distributional derivative and leads to desirable results when applied to image denoising, i.e., L-fitting with TGV penalty. The present paper studi...
متن کاملIll-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملTotal Variation Based Image Restoration of Three Dimensional Microscopic Objects
The inverse problem involving the determination of a three-dimensional biological structure from images obtained by means of optical-sectioning microscopy is ill-posed. Regularization methods must often be used in order to obtain a reasonable solution. Recently, the Total Variation (TV) regularization, as proposed b y Rudin, Osher and Fatemi [ll], has become very popular for this purpose. A n i...
متن کاملComplexity of linear ill-posed problems in Hilbert space
Information complexity of ill-posed problems may be seen as controversial. On the one hand side there were pessimistic results stating that the complexity is in nite, while on the other hand side the theory of ill-posed problems is well developed. In contrast to well-posed problems (continuous solution operators) the complexity analysis of ill-posed problems (discontinuous solution operators) i...
متن کامل