An improved exact filtered backprojection algorithm for spiral computed tomography

Proposed is a theoretically exact formula for inversion of data obtained by a spiral computed tomography scan with a two-dimensional detector array. The detector array is supposed to be of limited extent in the axial direction. The main property of the formula is that it can be implemented in a truly filtered backprojection fashion. First, one performs shift-invariant filtering of a derivative of the cone beam projections, and, second, the result is back-projected in order to form an image. Compared with an earlier reconstruction algorithm proposed by the author, the new one is two times faster, requires a smaller detector array, and does not impose restrictions on how big the patient is inside the gantry. Results of numerical experiments are presented.     

图像处理中全变差正则化数据拟合问题算法回顾

全变差正则化数据拟合问题产生于许多图像处理任务,如图像去噪、去模糊、图像修复、磁共振成像、压缩图像感知等.近年来,求解此类问题的快速高效算法发展很快.以最小二乘、最小一乘等为例简要回顾求解此类问题的主要算法,并讨论一个全变差正则化非凸数据拟合模型在脉冲噪声图像去模糊问题中的应用.     

Uniqueness of Gaussian quadrature formula for computed tomography

This note answers positively a question raised by B. Bojanov and G. Petrova. Namely, the Gaussian quadrature formula for computed tomography among the given type is unique.     

An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms

We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and show how it implies the Polydegree Conjecture. As the new conjecture is an ideal membership question, this shows that the Polydegree Conjecture is algorithmically decidable. We further describe how this approach provides a unified and shorter method of recovering existing results of Edo and Furter.     

An algorithmic approach for a special class of Markov chains

In this paper, we develop an algorithmic method for the evaluation of the steady state probability vector of a special class of finite state Markov chains. For the class of Markov chains considered here, it is assumed that the matrix associated with the set of linear equations for the steady state probabilities possess a special structure, such that it can be rearranged and decomposed as a sum of two matrices, one lower triangular with nonzero diagonal elements, and the other an upper triangular matrix with only very few nonzero columns. Almost all Markov chain models of queueing systems with finite source and/or finite capacity and first-come-first-served or head of the line nonpreemptive priority service discipline belongs to this special class.     

An electrical stimulation data based model to predict the healing period of fractured limb

ABSTRACT

In this work, diagnosing of reunion of human tibia fracture across limbs using a simple mathematical model is demonstrated. At present in practice, the fracture reunion is predicted using repeated radiographs. Frequent exposure to such radiation causes harmful health effects in patients. Hence, as an alternative, modelling technique using electrical data recorded across patients stimulated with DC electric voltage of range 0.1–1V is proposed. Various model structures, namely P1D and P1DZ models were tried. An error analysis was performed and it was observed that the measured data fitted P1DZ model with an error less than 5%. Model parameters namely process gain and time constant were observed. When the model parameter process gain becomes constant, the time constant reduces significantly indicating the healing of fracture. Reunion was also confirmed with simultaneously taken radiographs. The fact that human bone is a biological semi-conductor therefore exhibits electrical properties and bone does behave like a capacitor is proved by empirical methods in our study is the novelty of the work.     

An algorithmic construction of group automorphisms and the quantum Yang-Baxter equation

The structure group G of a non-degenerate symmetric set (X,S) is a Bieberbach and a Garside group. We describe a combinatorial method to compute explicitly a group of automorphisms of G and show this group admits a subgroup that preserves the Garside structure. In some special cases, we could also prove the group of automorphisms found is an outer automorphism group.     

Image reconstruction model for the exterior problem of computed tomography based on weighted directional total variation

The exterior problem of computed tomography (CT) is a special imaging modality and it is an important research issue in Non-Destructive Testing (NDT). In the exterior problem, the missing projection data vary with the position of the pixels. Furthermore, amounts of theoretical and experimental results showed that the edges that are tangent to the radial direction are much harder to be reconstructed than edges that are tangent to the angular direction. In this paper, a weighted directional total variation (WDTV) based regularization model was proposed to better deal with the exterior problem. By introducing the WDTV regularization term, our model can reconstruct high quality images. First, WDTV of an image also describes the sparsity of image gradient magnitude which can enforce the reconstructed result to be a nearly flat image. Second, our model can preserve edges and reduce artifacts near edges that are tangent to the radial direction. Third, a numerical implementation called SART+WDTV algorithm was developed to solve our model. Simulated and real experiments demonstrated that our model was more capable of suppressing artifacts and preserving edges.     

An algorithmic approach for maintenance management based on advanced state space systems and harmonic regressions

Point mechanisms are special track elements which failures results in delays and increased operating costs. In some cases such failures cause fatalities. A new robust algorithm for fault detection of point mechanisms is developed. It detects faults by comparing what can be considered the ‘normal’ or ‘expected’ shape of some signal with respect to the actual shape observed as new data become available. The expected shape is computed as a forecast of a combination of models. The proposed system deals with complicated features of the data in the case study, the main ones being the irregular sampling interval of the data and the time varying nature of the periodic behaviour. The system models are set up in a continuous-time framework and the system has been tested on a large dataset taken from a point mechanism operating on a commercial line.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

An effective strategy for the multibody simulation of jointed FE models in the framework of the floating frame of reference formulation.

In multibody systems (MBS), where elastic bodies are represented in the frame work of the ‘floating frame of reference formulation’ (FFRF), structural deformation is usually computed by the superposition of time invariant trial vectors (commonly called ‘modes’). However, the mode bases, which are discussed in the literature, do not take joints into special account at the stage of mode generation. In the presented paper we propose a problem–oriented extension of classical mode bases in order to consider the presence of joints. In the novel extension which we call ‘Joint Interface Modes’ (JIMs), Newton's 3rd law across the joint is taken into account at the stage of mode generation, which leads to a superior convergence at the stage of mode based computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An algorithmic approach to the construction of homomorphisms induced by maps in homology

This paper is devoted to giving the theoretical background for an algorithm for computing homomorphisms induced by maps in homology. The principal idea is to insert the graph of a given continuous map into a graph of a multi-valued representable map . The multi-valued representable maps have well developed continuity properties and admit a finite coding that permits treating them by combinatorial methods. We provide the construction of the homomorphism induced by such that . The presented construction does not require subsequent barycentric subdivisions and simplicial approximations of . The main motivation for this paper comes from the project of computing the Conley Index for discrete dynamical systems.

     

An algorithmic study of the Maximum Flow problem: A comparative statistical analysis

In this paper, we show the results of an experimental study about the most important algorithms proposed to solve the Maximum Flow problem. The appropriate statistical analysis not only allows us to justify comparisons between the different procedures but also to obtain classifications of their practical efficiency. Furthermore, an empirical experiment allows us to identify the influence of several parameters that are not included in a theoretical study.     

Optimization of a minimal-storage strategy for cloud amount data

A strategy is proposed which reduces the storage requirements for cloud amount information by up to 50%. Archiving only the mean cloud amount, μ, is recommended. Retrieval of most of the original data is possible if observations are made at high resolution ( 1 km) and the processing system gives rise to predominantly binary (i.e. cloud or no-cloud) information. The strategy is applicable to cloud amount at any level and to total cloud cover. One year's global cloud data can be stored on 2.5 computer magnetic tapes in contrast to the 13 tapes suggested by GARP/JOC (1980) and ISCCP (1982). The resultant new cloud archive will have the advantage of being equally useful for all scientific users (e.g. remote sensing and climate modelling groups) and each group's post-processing time will be greatly reduced.     

An integrodifferential indicator for the problem of single beam tomography

This article continues the authors’ study of the problem of X-ray tomography with few directions of the probing radiation. In the previous articles some special integrodifferential operators were used to process the available information. We propose a new formula for this operator, give theoretical justification of our algorithm, and include the results of appropriate simulations.