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The equations of rays and eikonal in finite differences are considered, taking into account the anisotropy of the refractive index. The paper presents a block diagram of the algorithm for choosing the variable of integration. The integration is carried out on the variable selected at the current step, which is assigned the specified step value. The increments of the remaining variables are calculated by expressions depending on the selected integration variable so that the increments on the remaining variables do not exceed the value of the integration variable. The integration variable is selected again and the increments are calculated. This method saves computational resources and minimizes the risk of transition to adjacent phase trajectories. The paper presents a general flowchart of the selection algorithm and expressions for calculating the increments of other variables at each step. The algorithm for calculating increments for each variable is demonstrated. The variable selection algorithm is developed for the case of a 7-dimensional phase space. It includes the projection of the pulse on the three axes of the Cartesian coordinate system, the projection of the coordinate and the phase component. The phase component describes the phase of the wave at the selected point and is analogous to the time dependence.
At reduction of the sizes of the distributing system, distance between its output reduce in once, in contrast with distance between radiators APAR. In such event corner deflections of the ray in DP APAR will corner of the deflection less in distributing system in n once also. For considered systems reduction factor of the geometric sizes n has formed the order 7. In corresponding to number once and was increased a corner of the deflection of the ray α in distributing system.
The research was conducted on a real array of data from energy consumption by 61 households over a period of 730 days. Classical regression analysis methods were compared with neural network analysis (trained with teacher).
The study was carried out on a three-dimensional mathematical phantom. For the reconstruction we used the algorithm of filtered reverse projections (Feldkamp algorithm) and algebraic reconstruction algorithm (ART). In the process of reconstruction, noise with a specified RMS was added to the data reflecting the angles of obtaining the projection, as well as the position of the focus point. The result of the study are the dependences of the normalized mean square error and the normalized absolute error of reconstruction for different layers from the NMS of the introduced noise.
The proposed method allows calculating the coefficients of the SART system matrix for only 2 planes, thus significantly reducing the computation time (up to 6-fold). Besides that, the amount of data stored decreases (approximately 295 times). This method allows performing parallel computations for each vertical layer in the reconstruction area, which provides a 10-fold gain in reconstruction rate.
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