Jörg Lampe

Fast reconstruction in magnetic particle imaging

Magnetic particle imaging (MPI) is a new tomographic imaging method which is able to capture the fast dynamic behavior of magnetic tracer material. From measured induced signals, the unknown magnetic particle concentration is reconstructed using a previously determined system function, which describes the relation between particle position and signal response. After discretization, the system function is represented by a matrix, whose size can prohibit the use of direct solvers for matrix inversion to reconstruct the image. In this paper, we present a new reconstruction approach, which combines efficient compression techniques and iterative reconstruction solvers. The data compression is based on orthogonal transforms, which extract the most relevant information from the system function matrix by thresholding, such that any iterative solver is strongly accelerated. The effect of the compression with respect to memory requirements, computational complexity and image quality is investigated. With the proposed method, it is possible to achieve real-time reconstruction with almost no loss in image quality using measured 4D MPI data.

On a quadratic eigenproblem occurring in regularized total least squares

A computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems has recently been proposed. Taking advantage of a variational characterization of real eigenvalues of nonlinear eigenproblems the existence of a real right-most eigenvalue for each quadratic eigenvalue problem in the sequence is proven. For large problems the approach is improved considerably utilizing information from the previous quadratic problems and early updates in a nonlinear Arnoldi method.

Global convergence of RTLSQEP: A solver of regularized total least squares problems via quadratic eigenproblems

Abstract The total least squares (TLS) method is a successful approach for linear problems if both the matrix and the right hand side are contaminated by some noise. In a recent paper Sima, Van Huffel and Golub suggested an iterative method for solving regularized TLS problems, where in each iteration step a quadratic eigenproblem has to be solved. In this paper we prove its global convergence, and we present an efficient implementation using an iterative projection method with thick updates.

Accelerating the LSTRS Algorithm

In a process for the extraction of celluloses from lignocelluloses, the extraction is carried out by means of heating with aqueous acetic acid under pressure and the addition of formic acid, whereby there is obtained a cellulose with a very low residual lignin content, which can be bleached with ozone and peracetic acid to high grades of white, and acetic and formic acid are recovered by means of distillation, so that waste waters do not, therefore, accumulate.

Large-scale Tikhonov regularization of total least squares

The total least squares (TLS) method is a successful approach for linear problems when not only the right-hand side but the system matrix is also contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we present a new approach for computing an approximate solution of the Tikhonov-regularized large-scale total least-squares problem. An iterative method is proposed which solves a convergent sequence of projected linear systems and thereby builds up a highly suitable search space. The focus is on efficient implementation with particular emphasis on the reuse of information.

Second Order Arnoldi Reduction application to some engineering problems

A standard approach to model reduction of second order linear dynamical systems is to rewrite the system as an equivalent first order system and then employ Krylov subspace techniques for model reduction. Recently the Second Order Arnoldi Reduction (SOAR) method was presented by Bai and Su which constructs the projection to a second order Krylov subspace thus preserving the structure of the underlying problem. In this paper we demonstrate the superior numerical behavior of the SOAR-algorithm upon the first order methods for four engineering problems from different areas.

Regularization of Large Scale Total Least Squares Problems

The total least squares (TLS) method is an appropriate approach for linear systems when not only the right-hand side but also the system matrix is contaminated by some noise. For ill-posed problems regularization is necessary to stabilize the computed solutions. In this presentation we discuss two approaches for regularizing large scale TLS problems. One which is based on adding a quadratic constraint and a Tikhonov type regularization concept.