When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill–posed operator equations, assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for. In fact, it is clear from works of Hegland, Engl a...

We establish theoretical convergence results for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a specific Tikhonov regularization. This Tikhnov regularization, which uses a seminorm generated by a linear operator, is motivated by mapping of the minimization variables to physical space which exposes the different scales of the parameters and therefore also suggests appropriate we...

We extend some previous results of ours [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use as a separating family of seminorms the absolute values of the components of the actions: with ...

In this papers we analyze the minimization of seminorms ‖L · ‖ on R under the constraint of a bounded I-divergence D(b,H ·) for rather general linear operators H and L. The I-divergence is also known as Kullback-Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Often H represents, e.g., a linear blur operator and L is some discrete d...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show equivalence function space vector field characterized by Gagliardo-type seminorm with 'projected difference' that corresponding Sobolev space. As an application, will use obtain Caccioppoli-type for nonlinear system nonlocal equations, which in turn is key ingredient a...

background: this study set out to evaluate the utility of cerebrovascular virtual non-contrast (vnc) scans. materials and methods: conventional non-contrast (cnc) and dual-energy computed tomography angiography (de-cta) head scans were conducted on 100 subjects, of which 46 were normal, 15 had parenchymal hematomas of the brain, 13 had ischemic infarction, 22 had tumors, and 4 had calcified les...

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...