In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences , by a trust region-cg algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while ...

In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences, by a trust region-CG algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while t...

We present a strategy for choosing the regularization parameter (Lepskij-type balancing principle) for ill-posed problems in metric spaces with deterministic or stochastic noise. Additionally we improve the strategy in comparison to the previously used version for Hilbert spaces in some ways. AMS-Classification: 47A52, 65J22, 49J35, 93E25

Given a compact operator G, we consider the ill-posed problem, given y , solve Gφ = y (approximately). Typically, in the presence of noise y / ∈ Range(G). We consider the iterated Tikhonov method for this problem. The method selects a regularization parameter based on stability and corrects several times to increase accuracy. We show that it gives a higher accuracy approximation to the noise-fr...

Doughnut Method We will calculate the dose deposited at the point P in the middle of the concentric circles. It can be calculated as the difference between the cases : first, the dose deposition by full big circle exposition, and second, the dose deposited when only full small circle is exposed : () () E E E Q f S dS Q f S dS p b s b b b S s s s S b s = − = − ∫ ∫ (A.1.1) where Eb and Es are abs...

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle for choosing regularization parameter are obtained.

We describe an approach to a class of ill-posed problems in which the determination of a ``lter' for obtaining approximate solutions is obtained by means of an optimization process. In Hilbert space settings a fairly explicit computation may be possible and this is presented. It is noted that, under certain conditions the resulting lter is, indeed, optimal in the sense of realizing a minimal un...

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by Neubauer [5]. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in t...

We consider an iterated form of Lavrentiev regularization, using a null sequence (αk) of positive real numbers to obtain a stable approximate solution for ill-posed nonlinear equations of the form F(x)= y, where F : D(F)⊆ X→ X is a nonlinear operator and X is a Hilbert space. Recently, Bakushinsky and Smirnova [“Iterative regularization and generalized discrepancy principle for monotone operato...