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In this chapter, a strip-method suitable for reducing pulse interference in communication channels, cryptography, steganography, and other applications is considered. The invariants to fragmentation and double-sided matrix transformation of images provide the noise immunity and transmission security. The chapter contains new definitions of invariants, as well as invariant images of the first and second types. Moreover, tasks of analyzing and synthesizing both invariants and corresponding transformation matrices are set forth too. The criteria of their existences are derived and methods for creation of invariant images using eigenvectors of transforming matrices are proposed. Some cases of complex and multiple eigenvalues of a direct transformation matrix are considered. It was proposed to solve the problem of finding the matrices of direct and inverse transformations by means of a given set of invariant images. The solution of the task of arraying the matrix of double-sided transformation according to a given set of invariant images is suggested.

The image quality influences the accuracy of obtained results. In the chapter, the application of the strip-method for noise-immune storage and transmission of images is analyzed. At the same time, before transmitting the matrix transformation of an original image has to be done, when the image fragments are mixed up and superimposed each other. The transformed image is transmitted over a communication channel, where it is distorted with a pulse noise, the latter being, for example, a possible reason for a complete loss of separate image fragments. After the signal transmission to the receiving end, an inverse transformation is performed. During this transformation, the reconstruction of the image takes place. If it is possible to provide a uniform distribution of the pulse noise over the whole area, which the image occupies without any changes of its energy, then a noticeable decrease of noise amplitude will take place and an acceptable quality of all fragments of the image are reconstructed. The tasks of the chapter are the consideration the versions of the two-sided strip-transformation of images and the choice of optimal transformation matrices. A great attention has been paid to the implementation of Hadamard matrices and matrices close to them such as Hadamard-Mersenne, Hadamard-Fermat, and Hadamard-Euler matrices.