The possibility of estimating the values of a function at given points of its domain is investigated. The estimation uses results of the measurements of a finite number of linear functionals; the results of the measurements are distorted by an error. It is shown that only the component of the functions from the linear finite-dimensional subspace can be estimated with a finite error. A method for estimating this component with accuracy control is proposed. The mathematical methods of measurement reduction proposed by Yu.P. Pyt’ev are used. An example of the estimation of an emission spectrum that is measured by a double-slit spectrometer is described.

In this paper, we studied the method for measuring the cloud bottom boundary altitude using the stereo pair of cloud images obtained using two digital photo cameras. We suggested a method for determining the camera orientation parameters using the nighttime images of star sky. The range to the cloud is calculated using the shift of the image of a cloud fragment as a whole. A given fragment on the photographs is identified using the methods of morphological image analysis. When the stereo base is 60 m and images are taken with a resolution of 1200 pixels within a field of view of 60°, the uncertainty does not exceed 10% when cloud altitude is less than 4 km. Optimizing the parameters of photography and increasing the stereo base may substantially improve the accuracy of the cloud base altitude estimation. Examples are presented of cloud bottom boundary determination using a prototype of the experimental setup as compared to data of a laser range finder.

Based on the morphological analysis techniques developed under the guidance of Yu.P. Pyt’ev, a method for filtering time series is proposed that is capable of detecting an almost cyclic component with a varying cycle length and varying series members within cycles. The effectiveness of the approach is illustrated as applied to decomposition of time series of atmospheric СО₂ concentrations. After filtering out the series component responsible for diurnal variability, the series residual becomes stationary, so mathematical statistical methods and Fourier analysis can be used for its further investigation. The results are verified by comparing them with Fourier analysis data. A cyclicity with a period longer than one day is studied using Fourier expansion and wavelet analysis of the original series.

We propose a lightweight noise-canceling filtering neural network that implements the filtering stage in the algorithm for tomographic reconstruction of convolution and backprojection (Filtered BackProjection—FBP). We substantiate the neural network architecture, selected on the basis of the possibility of approximating the ramp filtering operation with sufficient accuracy. The network performance has been demonstrated using synthetic data that mimics low-exposure tomographic projections. The quantum nature of X-ray radiation, the exposure time of one frame, and the nonlinear response of the ionizing radiation detector are taken into account when generating the synthetic data. The reconstruction time using the proposed network is 11 times shorter than that of the heavy networks selected for comparison, with the reconstruction quality in the \(SSIM\) metric above 0.9.