RESUMEN

The paper presents research on a specific approach to the issue of computed tomography with an incomplete data set. The case of incomplete information is quite common, for example when examining objects of large size or difficult to access. Algorithms devoted to this type of problems can be used to detect anomalies in coal seams that pose a threat to the life of miners. The most dangerous example of such an anomaly may be a compressed gas tank, which expands rapidly during exploitation, at the same time ejecting rock fragments, which are a real threat to the working crew. The approach presented in the paper is an improvement of the previous idea, in which the detected objects were represented by sequences of points. These points represent rectangles, which were characterized by sequences of their parameters. This time, instead of sequences in the representation, there are sets of objects, which allow for the elimination of duplicates. As a result, the reconstruction is faster. The algorithm presented in the paper solves the inverse problem of finding the minimum of the objective function. Heuristic algorithms are suitable for solving this type of tasks. The following heuristic algorithms are described, tested and compared: Aquila Optimizer (AQ), Firefly Algorithm (FA), Whale Optimization Algorithm (WOA), Butterfly Optimization Algorithm (BOA) and Dynamic Butterfly Optimization Algorithm (DBOA). The research showed that the best algorithm for this type of problem turned out to be DBOA.

Asunto(s)

Carbón Mineral , Heurística , Algoritmos , Tomografía Computarizada por Rayos X

RESUMEN

Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devices, smart home, smart transportation and the like. Therefore, there is a need to look for some new techniques for solving the problems described by means of the appropriate equations, including differential equations, integral equations and integro-differential equations. The object of interests of this paper is the method dedicated for solving some integro-differential equations with a retarded (delayed) argument. The proposed procedure is based on the Taylor differential transformation which enables to transform the given integro-differential equation into a respective system of algebraic (nonlinear, very often) equations. The described method is efficient and relatively simple to use, however a high degree of generality and complexity of problems, defined by means of the discussed equations, makes impossible to obtain a general form of their solution and enforces an individual approach to each equation, which, however, does not diminish the benefits associated with its use.

RESUMEN

Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful.