6533b853fe1ef96bd12accbb

RESEARCH PRODUCT

New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing

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Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team by applying them to image processing problems such as compression, progressive transmission and watermarking.