K.Yu. Prokhorov1, A.N. Buchatsky2, G.G. Rogozinski3

1,2 Bonch-Bruevich Saint-Petersburg State University of Telecommunications (St. Petersburg, Russia)

3 N.S. Solomenko Institute of Transport Problems of the Russian Academy of Sciences (St. Petersburg, Russia)

1 kuprokhorov@gmail.com, 2 alexanderbuchatsky@yandex.ru, 3 gleb.rogozinski@gmail.com

This work presents a comprehensive analysis of structural transformations in image synthesis via the 2D Inverse Packet Discrete Wavelet Transform (IPDWT). We address the challenge of controlling spatial properties of the output by formalizing the relationship between the types of wavelet coefficients used for reconstruction and the resulting image shifts and symmetries. A quantitative spatial shift model is developed and verified, establishing a deterministic link between the coefficient type and the direction of induced displacement. A procedure for predicting cumulative displacement in multi-level reconstruction is also proposed. Using a modified "Wavelet Noise" algorithm, we experimentally discovered and classified the group structure of all possible reconstructions. Two distinct grouping types were identified, dependent on the seed pattern's symmetry. For symmetric patterns, transformations between reconstructions are visually indistinguishable from the actions of the dihedral group D₄. For asymmetric patterns, a full commutative group structure of shift operations is manifested, hypothetically isomorphic. The results provide a fundamental algebraic framework for the IPDWT algorithm, enabling deterministic control over image and texture synthesis. This opens new possibilities for applications in computer graphics and machine learning, such as predictable generation of structural patterns and texture analysis.

Prokhorov K.Yu., Buchatsky A.N., Rogozinski G.G. Structural transformations in inverse packet wavelet transform: spatial shift model and group classification of reconstructions // Radioengineering. 2026. V. 90. № 9. P. 41−53. DOI: https://doi.org/10.18127/j00338486-202609-04

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