Fast OPED algorithm for reconstruction of images from Radon data

A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of the fast implementation is proved under the condition that the function is mildly smooth. The numerical test shows that the accuracy of the OPED algorithm changes little when the fast implementation is used.Comment: 13 page

OPED reconstruction algorithm for limited angle problem

The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems. In stead of completing the set of data, the set of discrete sine transforms of the data is completed. This is achieved by solving systems of linear equations that have, upon choosing appropriate parameters, positive definite coefficient matrices. Numerical examples are presented.Comment: 17 page

Approximation and Reconstruction from Attenuated Radon Projections

Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for reconstructing two dimensional functions (images) from attenuated Radon projections. Similar results are established for reconstructing functions on the sphere from projections described by integrals over circles on the sphere, and for reconstructing functions on the three-dimensional ball and cylinder domains.Comment: 25 pages, 3 figure

Zwangskräfte bei einem Mehrkörpersystem mit drei Freiheitsgraden

A mechanical system with three degrees of freedom in a gravitational field is analyzed for chaotic versus regular behavior, and for moments of constraint that act on its axes. The system consists of three connected rigid bodies each of which rotating about one axes. The vertical axis of the first body is fixed to the immobile base; the second body rotates about a horizontal axis which moves with the first, and the third body rotates about an axis in the second. Its moments of inertia A, B, C are assumed to obey C=A B. The motion is regular if the body is symmetric, A=B, otherwise the asymmetry parameter µ=(B-A)/B determines the degree of chaoticity. The different types of motion were identified with the help of Poincaré sections while the study of forces of constraints as functions of time was carried out using methods of time-frequency analysis: Fourier analysis in the case of regular, and wavelet analysis in the case of chaotic motion. It was noticed that for large values of µ the motion of the system shows an effect that can be described as intermittency, that is, there exist of long phases of motion during which the system behaves regularly. The reason for the occurence of such an effect is explained. It is observed that the forces of constraints obtain their maximal values in connection with the transition from one regular phase to another. In spite of the presence of chaos in the Poincaré-sections, for large intervals of µ, the wavelet transformation diagrams reflect a relatively regular behavior of the forces of constraints. Using classical statistical methods it would be possible, on the basis of analysis, to evaluate the long-term effects of chaotic motion on the wearing of materials in the bearings of the system

Forces of constraints in a manybody system with three degrees of freedom

A mechanical system with three degrees of freedom in a gravitational field is analyzed for chaotic versus regular behavior, and for moments of constraint that act on its axes. The system consists of three connected rigid bodies each of which rotating about one axes. The vertical axis of the first body is fixed to the immobile base; the second body rotates about a horizontal axis which moves with the first, and the third body rotates about an axis in the second. Its moments of inertia A, B, C are assumed to obey C=A B. The motion is regular if the body is symmetric, A=B, otherwise the asymmetry parameter µ=(B-A)/B determines the degree of chaoticity. The different types of motion were identified with the help of Poincaré sections while the study of forces of constraints as functions of time was carried out using methods of time-frequency analysis: Fourier analysis in the case of regular, and wavelet analysis in the case of chaotic motion. It was noticed that for large values of µ the motion of the system shows an effect that can be described as intermittency, that is, there exist of long phases of motion during which the system behaves regularly. The reason for the occurence of such an effect is explained. It is observed that the forces of constraints obtain their maximal values in connection with the transition from one regular phase to another. In spite of the presence of chaos in the Poincaré-sections, for large intervals of µ, the wavelet transformation diagrams reflect a relatively regular behavior of the forces of constraints. Using classical statistical methods it would be possible, on the basis of analysis, to evaluate the long-term effects of chaotic motion on the wearing of materials in the bearings of the system

The dc motors with smooth armature and excitation from the high- coercive constant magnets

The object of investigation: the DC low-power motors with smooth armature and high-coercive constant magnets (DCMSA). The new constructions of the DCMSA and of a smooth armature have been developed as well as the mathematical models for the design of the DCMSA and of the magnetic field. Suggested have been the formulae for the inductances, interinductances in the winding, magnet height designs; the dependences of the correction coefficients at the design of the MMF drops on the rest areas. The DCMSA have been run in the production and have been used as the drives of the equipment, machines, tools. The developed methods of the DCMSA electromagnetic design and the obtained formulae and dependences can be used in the process of their design and investigation. The developed DCMSA of the CKIT type have been run in the production. The economy obtained from the manufacture of DCMSA instead of DPT, series 2P only due to the reduction of expenditures for materials and labour, consists 50 to 60 mln roubles at the plan program of 20,000 pcs/year (prices of July 1, 1992)Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

IMAGE RECONSTRUCTION BY OPED ALGORITHM WITH AVERAGING

Abstract. OPED is a new image reconstruction algorithm based on orthogonal polynomial expansion on the disk. We show that the integral of the approximation function in OPED can be given explicitly and evaluated efficiently. As a consequence, the reconstructed image over a pixel can be effectively represented by its average over the pixel, instead of by its value at a single point in the pixel, which can help to reduce the aliasing caused by under sampling. Numerical examples are presented to show that the averaging process indeed improves the quality of the reconstructed images. 1