Antropov O. Restoration of corrupted signals and images with use of the nonquadratic regularization.

The problem of corrupted signal and image restoration of radiophysical origin with use of the nonquadratic regularization methods is considered in the thesis. The object is signal and image restoration within inverse radiophysic problem solution. Purpose of the work is increase of quality and sustainability of signal and image restoration while processing physical measurements results in spatioral and frequency domain in presence of noise with unknown spectral and statistical characteristics. Methods: ill-posed problem solution, spectral analysis, linear algebra, reflectometry microwave measurements. The problem of continuous signals restoration in presence of unknown pulses was solved by minimization of the quasinorm of approximation error between estimated and measured dependencies. The problem of extrapolation of multifrequency reflection coefficient data for the layered dielectric structure was effectively solved, allowing for enhancement of reliability and precision of estimation of structure parameters through synthesized time signals analysis and interpretation. On the basis of developed multifrequency reflection coefficient data extrapolation procedure the modification of Fourier-holography approach for restoration of complex reflection coefficient of dielectric layered structures on the basis of scalar measurements was proposed and realized experimentally, resulting in more precise restoration of complex reflection coefficient and simplifying the procedure. Method for restoration of finite and piecewise-constant signals and images is developed. Appropriate method is used afterwards for enhancement of restoration results for antenna pattern via inverse problem solution for currents. Another application of developed restoration method is effective filtration of noised satellite images and electrodynamical images of objects. Area - radiowave nondestructive testing, remote sensing, antenna measurements, study courses.