Structural resonance methods for image processing and pattern recognition

We have developed group-theoretical methods of structural resonance by analogy with “resonance methods” applied in the classical theory of oscillations and waves and in quantum physics. The “structural-resonance approach” is one of the advantageous interpretations of the reconstructive computerized diagnostics based on the previously developed group-theoretical statistical approach to solve ill-posed inverse problems. We have elaborated a unified method of reconstructing a “heterogenous” test-object with wide semantic spectrum, regarding this object as a “semantic mixture” of different mutually complementary semantic contents, matching each of them with its formalized invariant structure. To separate a cleared semantic content from the “mixture”, it is necessary to apply operators from its group of automorphisms to the informational image of the “mixture”. It results in randomization of all other semantic contents, so they can be easily suppressed statistically. We have defined measures of intensity for such resonance, carried out a detailed comparison of tomosynthesis and such structural-resonance “sense synthesis”, and compared “material reconstruction” and reconstruction of structural-functional connections. Finally yet importantly, we have discussed prospects of these methods for solving ill-posed problems in various fields of science and practice.