Abstract
Tensor representation of video sequences or 3D images becomes very popular recently. Despite certain advantages, the main obstacle for the wide application of this approach is the high computational complexity. In the paper is presented new method for third-order tensor representation in the spectrum space of the 3D-Walsh–Hadamard Transform (WHT). To lessen the computational complexity, here is used pyramidal decomposition based on the 3D WHT with Reduces Inverse Spectrum Pyramid (RISP). In result is achieved high concentration of the tensor energy in a minimum number of spectrum coefficients, most of which—in the first (lowest) decomposition level. After the processing, the tensor is transformed into a multi-level spectrum tensor of same size. The proposed representation has low computational complexity because its execution needs operations like “addition” only. The specific properties of the 3D-RISP permit it to be used in various application areas which require parallel processing and analysis of 3D data represented as third-order tensors: sequences of correlated images (video, multi-spectral, multi-view, various kinds of medical images), multichannel signals, huge massifs of data, etc.
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Acknowledgements
This work was supported by the National Science Fund of Bulgaria: Project No. KP-06-H27/16 “Development of efficient methods and algorithms for tensor-based processing and analysis of multidimensional images with application in interdisciplinary areas”.
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Kountchev, R., Kountcheva, R. (2020). Low Computational Complexity Third-Order Tensor Representation Through Inverse Spectrum Pyramid. In: Kountchev, R., Patnaik, S., Shi, J., Favorskaya, M. (eds) Advances in 3D Image and Graphics Representation, Analysis, Computing and Information Technology. Smart Innovation, Systems and Technologies, vol 179. Springer, Singapore. https://doi.org/10.1007/978-981-15-3863-6_8
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DOI: https://doi.org/10.1007/978-981-15-3863-6_8
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