M. : PHYSMATLIT, 2008. - 496 s. - ISBN 978-5-9221-0841-6 . , under ed. A. A. Potapova . The monograph for the first time systematically considered and generalized the new directions developed by the authors in the application of the theory of processing distorted and low-contrast images to the current problems of radiophysics, astronomy, optics and radar. The monograph consists of two parts. In the first part, on the basis of the apparatus of the integer Lebesgue measure, a theoretical analysis of the uniqueness of the restoration of one-dimensional signals and images by incomplete information about their Fourier spectra was carried out. Models based on the use of the Hilbert transform for communication between the module and the phase in a two-dimensional case. In the absence of conditions for analytical solution of problems, methods of projections on convex sets are used. For professionals interested in new ideas and modern methods of image processing, signals and pattern recognition, as well as for graduate students and students of relevant specialties