The main tissue parameters targeted by MR tomography include, among others, relaxation times T₁ and T₂. This paper focuses on the computation of the relaxation time T₂ measured with the Spin Echo method, where the sensing coil of the tomograph provides a multi-echo signal. The maxima of these echoes must be interleaved with an exponential function, and the T₂ relaxation can be determined directly from the exponential waveform. As this procedure needs to be repeated for each pixel of the scanned tissue, the processing of large images then becomes very intensive. For example, given the common resolution of 256×256 with 20 slices and five echoes at different times T_E, it is necessary to reconstruct 1.3∙10⁶ exponential functions. At present, such computation performed on a regular PC may last even several minutes. This paper introduces the results provided by accelerated computation based on parallelization and carried out with a graphics card. By using the simple method of linear regression, we obtain a processing time of less than 36 ms. Another effective option consists in the Levenberg-Marquardt algorithm, which enables us to reconstruct the same image in 96 ms. This period is at least 900 times shorter than that achievable with professional software. In this context, the paper also comprises an analysis of the results provided by the above-discussed techniques.

This paper discusses the optimization of domain parameters in electrical impedance tomography-based imaging. Precise image reconstruction requires accurate, well-correlated physical and numerical finite element method (FEM) models; thus, we employed the Nelder–Mead algorithm and a complete electrode model to evaluate the individual parameters, including the initial conductivity, electrode misplacement, and shape deformation. The optimization process was designed to calculate the parameters of the numerical model before the image reconstruction. The models were verified via simulation and experimental measurement with single source current patterns. The impact of the optimization on the above parameters was reflected in the applied image reconstruction process, where the conductivity error dropped by 6.16% and 11.58% in adjacent and opposite driving, respectively. In the shape deformation, the inhomogeneity area ratio increased by 11.0% and 48.9%; the imprecise placement of the 6th electrode was successfully optimized with adjacent driving; the conductivity error dropped by 12.69%; and the inhomogeneity localization exhibited a rise of 66.7%. The opposite driving option produces undesired duality resulting from the measurement pattern. The designed optimization process proved to be suitable for correlating the numerical and the physical models, and it also enabled us to eliminate imaging uncertainties and artifacts.

The paper deals with modern methods of image processing, especially image segmentation, classification and evaluation of parameters. It is focused primarily on processing medical images of soft tissues obtained by magnetic resonance tomography (MR). It is easy to describe edges of the sought objects using of segmented images. The edges found can be useful for further processing of monitored object such as calculating the perimeter, surface and volume evaluation or even three-dimensional shape reconstruction. The proposed solutions can be used for the classification of healthy/unhealthy tissues in MR or other imaging. Application examples of the proposed segmentation methods are shown. Research in the area of image segmentation is focused on methods based on solving partial differential equations. This is a modern method for image processing, often called the active contour method. It is of great advantage in the segmentation of real images degraded by noise with fuzzy edges and transitions between objects. In the paper, results of the segmentation of medical images by the active contour method are compared with results of the segmentation by other existing methods. Experimental applications are given which demonstrate the very good properties of the active contour method.Článek se zabývá moderními metodami zpracování obrazů, konkrétně segmentací obrazů, klasifikací a vyhodnocením parametrů. Je zaměřen primárně na zpracování medicínských obrazů měkkých tkání pořízených magneticko-rezonanční tomografií (MR). Segmentované obrazy slouží k popisu hran hledaných objektů. Hrany mohou být užitečné pro další zpracování hledaných oblastí jako je výpočet obvodu, povrchu, objemu nebo dokonce pro trojrozměrnou rekonstrukci. Navrhovaná řešení mohou být použity pro klasifikaci zdravých/postižených tkání pomocí MR nebo dalších technik. Jsou ukázány příklady aplikací. Výzkum v oblasti segmentace obrazů je zaměřen na metody založené na řešení parciálních diferenciálních rovnic. Jde o moderní metody zpracování obrazů, často nazývané metody aktivních kontur. Mají velmi dobré výsledky při segmentování reálných obrazů zatížených šumem, hladkými přechody mezi oblastmi a rozmazanými hranami. V článku jsou srovnány výsledky segmentace medicínských obrazů metodou aktivních kontur s dalšími metodami. Jsou uvedeny experimentální aplikace, které ukazují velmi dobré vlastnosti metody aktivních kontur

The paper discusses mathematical tools to evaluate novel noise spectroscopy based analysis and describes, via physical similarity, the mathematical models expressing the quantitative character of the modeled task. Using the Stefan–Boltzmann law, the authors indicate finding the spectral density of the radiated power of a hemisphere, and, for the selected frequency interval and temperature, they compare the simplified models with the expression of noise spectral density according to the Johnson–Nyquist formula or Nyquist’s expression of the function of spectral density based on a derivation of Planck’s law. The related measurements and evaluations, together with analyses of the noise spectroscopy of periodic resonant structures, are also outlined in the given context.

The present paper discusses the process of parallelizing an algorithm for the reconstruction of an image acquired via electrical impedance tomography (EIT). The introductory section comprises a general description of EIT, the inverse problem, and regularization; in this context, the potential of the method for biomedicine, defectoscopy, and geophysical mapping is outlined. The following chapter then analyzes the objective function of the EIT inverse problem together with Tikhonov regularization. Besides setting up the objective function with a regularizing member, the authors also specify the differentiation equation for the iterative solution of the inverse problem via the Gauss-Newton method. Further, the time consumption of computing the Jacobian via a CPU compared to using a newly assembled program that exploits GPU-based parallel processing is investigated in detail. The program, utilizing the NVIDIA CUDA platform, employs parallelized computation of the individual columns of the Jacobi matrix, and this approach proved to be twenty times faster than the CPU-based sequential processing.