PURPOSE In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm. METHODS Based on the formulation of the iterative Landweber algorithm, a frequency domain window function is derived fo...

The purpose of this paper is to give a new presentation of some of the main results concerning Landweber exactness in the context of the homotopy theory of stacks. We present two new criteria for Landweber exactness over a flat Hopf algebroid. The first criterion is used to classify stacks arising from Landweber exact maps of rings. Using as extra input only Lazard’s theorem and Cartier’s class...

A fundamental theorem of Büchi and Landweber shows that the Church synthesis problem is computable. Büchi and Landweber reduced the Church Problem to problems about ω-games and used the determinacy of such games as one of the main tools to show its computability. We consider a natural generalization of the Church problem to countable ordinals and investigate games of arbitrary countable length....

This paper presents an empirical comparison of the Landweber iterative image restoration method with the direct CLS method, with the goal of determining which is more robust against errors in the estimated point spread function. 1. Image Formation Process 2. Restoration Methods q Constrained Least Squares (direct) ( ) T T T cls H C C H H h 1 − + = a q Landweber (iterative) ) ˆ ( ˆ ˆ * 1 k k k f...

We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for the Landweber iterations on a Hilbert space.

This is a review paper addressing two main aspects of DNA computing research: DNA computing in vitro (in the test tube) and in vivo (in a living organism). We describe the first successful in vitro DNA computing experiment [L.M. Adleman, Science 266 (1994) 1021–1024] which solved a mathematical problem, the Directed Hamiltonian Path Problem, solely by manipulation of DNA strands in test tubes. ...

Atmospheric tomography is a prerequisite step before wavefront perturbations can be corrected in Multi Conjucate Adaptive Optics (MCAO) systems. Recently, the use of a Landweber-Kaczmarz iteration has been proposed to solve the tomography problem. However, due to the geometric partitioning of the update steps in this method, discontinuities in the solution appear that are physically implausible...

In recent years Landweber(-Kaczmarz) method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. I...

Electrical capacitance tomography (ECT) is a non-invasive imaging technique that aims at visualization the permittivity distribution of dielectric materials based on the measured capacitances. In this paper, the 3D finite element models of a direct 3D ECT sensor with or without dielectric spheres inside the sensor are set up by using finite element modeling. The sensitivity analysis of the sens...