Search results for "Kolmogorov superposition theorem"
showing 4 items of 4 documents
A new Adaptive and Progressive Image Transmission Approach using Function Superpositions
2010
International audience; We present a novel approach to adaptive and progressive image transmission, based on the decomposition of an image into compositions and superpositions of monovariate functions. The monovariate functions are iteratively constructed and transmitted, one after the other, to progressively reconstruct the original image: the progressive transmission is performed directly in the 1D space of the monovariate functions and independently of any statistical properties of the image. Each monovariate function contains only a fraction of the pixels of the image. Each new transmitted monovariate function adds data to the previously transmitted monovariate functions. After each tra…
Progressive transmission of secured images with authentication using decompositions into monovariate functions
2014
International audience; We propose a progressive transmission approach of an image authenticated using an overlapping subimage that can be removed to restore the original image. Our approach is different from most visible water- marking approaches that allow one to later remove the watermark, because the mark is not directly introduced in the two-dimensional image space. Instead, it is rather applied to an equivalent monovariate representation of the image. Precisely, the approach is based on our progressive transmission approach that relies on a modified Kolmogorov spline network, and therefore inherits its advantages: resilience to packet losses during transmis- sion and support of hetero…
Kolmogorov superposition theorem for image compression
2012
International audience; The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trad…
New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing
2012
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…