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The method of the spectral singular analysis of two-dimensional fields of deliberately distorted digital images (2D-SSA)


V.N. Nikolaev - Dr.Sc. (Eng.), Professor, Department Department of information systems and technologies, Southwest State University (Kursk). E-mail: T.I. Lapina - Ph.D. (Eng.), Associate Professor, Head of Department of information systems and technologies, Southwest State University (Kursk). E-mail: P.V. Grishin - Post-graduate Student, Department of information systems and technologies, Southwest State University (Kursk)

An important problem in the field of information technology is to assess the reliability of digital images (DI), used in various automated systems, geographic information systems, global computer network Internet. One of the reasons of possible changes of DI, in a variety of formats is the wide availability of professional digital image processing (bitmap editors) to landlines and mobile computing systems and devices. Common manipulation aimed at falsifying information, is a insert in the main DI of the plots with another image. When performing insert operations are applied to digital image processing: smoothing edges, harmonization of scale, rotation angle and brightness of the insert with the main image, and in some cases elimination of the visually noticeable contradictions, for example, associated with the direction of shadows or light objects surface. Such manipulations implement different types of spatial filtering of the image - this leads to a change in the frequency spectrum of a local region image to \"background\" its undistorted part, which is a sign of deliberate distortion of DI. The purpose of this paper is to study possibilities of the method of singular spectral analysis of two-dimensional fields of 2D-SSA (2-D Singular Spectrum Analysis) to detect signs of the presence of the insertion in DI. Considered a deliberate distortion of DI in terms of the two-dimensional scalar fields. Field subjected to deliberate distortion in accordance with the specified functions. Method 2D-SSA is used to decompose a two-dimensional field into a sum of its additive component, with no a priori specified models of these components. To check this assumption, experimental research method, 2D-SSA. The algorithm that implements the method of 2D-SSA consists of two stages: decomposition and reconstruction, each of which consists of two steps. The first (decomposition) - the construction of the trajectory matrix and its singular value decomposition. The second (recovery) - group own triples and the design of the grouped component. Identified two possible options using the method of 2D-SSA: the first involves restoring the DI of the noise component and further statistical analysis; the second option is to analyze the values of the eigenvalues of singular value decomposition of segments (Podiatric) DI. The study shows that in order to detect deliberate distortion of DI, it is advisable to use the method of 2D-SSA to restore the noise component of the image. Consideration of the stationarity of the noise allows to detect the fact of changing this condition in any region that is a sign of deliberate distortion. The results showed that with decrease of the ratio signal/noise of the image, the probability of detecting the intentional distortion, using the method of 2D-SSA, increases. It is shown that the use of the method of 2D-SSA can significantly reduce the complexity of detecting the intentional distortion of images. It is established that the second variant of application of the method of 2D-SSA contains a smaller number of computational operations that, in General, significantly increases the efficiency of detecting the intentional dis-tortion. Studies have shown that the method of 2D-SSA can be used as the basis to detect deliberate distortion of DI imple-mented pasting from another image.


  1. Nikolaev V.N.Metodologija postroenija i ispolzovanija innovacionnykh geoinformacionnykh sistem // Kursk: Izdatelstvo JUZGU. 2014. 166 s.
  2. Nikolaev V.N.Tekhniko-ehkonomicheskie modeli geoinformacionnykh sistem nauchno-proizvodstvennykh predprijatijj // Kursk: Izdatelstvo JUZGU. 2015. 220 s.
  3. Nikolaev V.N., Urjaseva M.V. Vlijanie Veb-sajjta VUZa na ego konkurentosposobnost // Sb. mat. I reg. NTK «Informacionnye sistemy i tekhnologii», g. Kursk, JUZGU, 2012. S. 80–82.
  4. Nikolaev V.N., Valivakhin V.V. Reinzhiniring sistemy informacionnogo obespechenija funkcionirovanija telekommunikacionnojj kompanii // Sb. nauchnykh trudov 4-jj Mezhdunar. NPK «Innovacii, kachestvo i servis v tekhnike i tekhnologijakh», g. Kursk, JUZGU, 2014. T. 2. S. 54–58.
  5. Sencar H., Memon N. Over view of state-of-the-art in digital image forensics // Department of computer and in formation science, Polytechnic University, Brooklyn, USA. 2007.
  6. Goljandina N.EH., Usevich K.D. Metod 2D-SSA dlja analiza dvukhmernykh polejj // Sb. trudov VII Mezhdunar. konfer. «Identifikacija sistem i zadachi upravlenija». 2008. S. 1657–1727.
  7. Demmel Dzh.Vychislitelnaja linejjnaja algebra. Teorija i prilozhenija. M.: Mir. 2001. 430 s.
  8. Gonsales R., Vuds R. Cifrovaja obrabotka izobrazhenijj. M.: Tekhnosfera. 2005. 1072 s.
  9. Goljandina N.EH.Metod «Gusenica»-SSA analiz vremennykh rjadov. Uchebnoe posobie. SPb. 2004. 76 s.


May 29, 2020

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