Signals and Image Processing in Information Systems by Tensor Analysis Methods

The paper deals with the problem of signal and image processing by means of tensor analysis. Within the framework of the considered approach, a short review of existing methods is given, which includes general approaches such as the principal component analysis, independent component analysis, canonical correlation analysis, and particular practical problems, which include blind signal separation and image compression. All these methods are united by the need to perform a singular value decomposition operation, for which the input data must be structured by a matrix or their sequence. Reducing the size of the core matrix representation by discarding non-essential components allows you to present data in a compact form. Joint diagonalization of a sequence of matrices produces satisfactory results assuming that the data or signal sets are statistically independent. The presented data are considered in two examples, allowing us to clearly assess the advantage of the presented approach.