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Optical location systems implemented on the basis of high-resolution video cameras are currently used in many areas. These are, for example, medical equipment, traffic control systems, satellite monitoring systems, preventive security systems, object recognition and classification systems, etc. For these systems, the requirements for high-resolution image processing speed of 8K, 16K and more are increasing every year. Processing of such information becomes even more difficult when providing a reading of high frequency frames from the matrix of the video camera, especially for systems operating in real time and using high-speed networks of exchange, processing and integration of information. This requires to determine a set of types of information processing procedures: masking, compression, noise-protected coding, etc., for which algorithms should be revised in multi-user and multiposition application in distributed information processing and aggregation systems. Processing of such information becomes even more difficult when providing a high frequency of reading frames from the matrix of the video camera, especially for systems operating in real time and using high-speed networks of exchange, processing and integration of information. This requires to determine a set of types of information processing procedures: masking, compression, noise-protected coding, etc., for which algorithms should be revised in case of multi-user and multiposition application in distributed information processing and aggregation systems. In this regard, the problems of development and improvement of new ways of representation, compression, storage, masking and error-correcting coding of high-resolution images with a common mathematical basis are relevant. Most information transformation procedures are based on the use of orthogonal bases, in particular orthogonal and quasiorthogonal matrices. The paper presents the results of the search and formation of such bases, the methods of synthesis of quasi-orthogonal matrices for image processing problems that meet the formulated requirements. The methods of guaranteed synthesis of matrices of symmetric, cyclic, block-cyclic and other structures of different orders, assuming economical storage and generation, are proposed. Such matrix bases, which are constantly expanding, provide developers with a wide range of algorithms to choose the most appropriate one from them. The problem of search and study of extreme quasi-orthogonal matrices has great importance for a wider range of information processing tasks, not just images. The proposed mechanisms for finding new classes of matrices allow creation and development of competitive methods of storage, presentation, compression, noise-resistant coding of data during their transmission in wireless high-speed networks of exchange, processing and aggregation. The results of the work correspond to the world level of research and have a universal character, as they can be applied in a variety of fields, including orthogonal cryptography, models of crystallography and biology, in the finite models of dynamic processes, etc.
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