Direct and reverse tasks of restoring images, spectroscopy and tomography with Matlab. + CD

The book sets out the application of the apparatus of integrated equations (IU), systems of linear algebraic equations (SLAU) and systems of linear-uneline equations (Slnu), as well as software tools of the Matlab system to solve a number of iconica’s application tasks (recovery of images using computers), spectroscopy and spectroscopy and tomography. Direct and reverse tasks of restoring distorted (lubricated, defocused, scolded) images, spectroscopy (restoration of continuous and discrete spectra) and two types of tomography: X -ray computed tomography (RCT) and infrared tomography (ICT) are presented. Reverse tasks are described mainly by the integrated equations of Fredgolm I, the problem of the solution of which is incorrect, therefore, the equations are solved by Tikhonov’s regulatory, as well as the viner parametric filtration method. Methods and numerical algorithms are brought to programs in the Matlab system. Listings of programs and the results of processing model and real data are given. In relation to the problem of iconics, both well-known methods of recovery of images and the method developed by the author called "truncation- blur-rotation", as well as the supercretion method, rapid algorithms for eliminating lubrication, and spectral way to evaluate the distortion parameters developed. A new type of noise is proposed - multipolar impulse noise and a way of filtering it. A new methodology for solving the reverse problem of spectroscopy has been set out - a method of training, or modeling for a continuous spectrum case and an integral approximation algorithm for a discrete spectrum case. The presentation of the known RCT methods is supplemented by the presentation of the little -known method of Arsenin, based on the bringing of July Radon to IU Fredgolm. When solving the problems of IR tomography, an original generalized method for solving singular integral equations (SIUs) was used.
For bachelors, undergraduates, graduate students of universities studying in the areas of training and specialties included in the UGS: "Mathematics and Mechanics"," Computer and Information Sciences", "Physics and Astronomy", "Informatics and Computing Technology", " Photonics, instrumentation, optical and biotechnical systems and technologies. " The book will be useful to teachers and researchers in the fields of fundamental, computing