0000000001082123
AUTHOR
Pierre-emmanuel Leni
showing 3 related works from this author
Nouvelles méthodes de traitement de signaux multidimensionnels par décomposition suivant le théorème de Superposition de Kolmogorov
2010
The processing of multidimensional signal remains difficult when using monodimensional-based methods. Therefore, it is either required to extend monodimensional methods to several dimensions, which is not always possible, or to convert the multidimensional signals into 1D signals. In this case, the priority is to preserve most of the properties of the original signal. In this context, the Kolmogorov Superposition Theorem offers a promising theoretical framework for multidimensional signal conversion. In 1957, Kolmogorov demonstrated that any multivariate function can be written as sums and compositions of monovariate functions.We have focused on the image decomposition according to the supe…
The Kolmogorov superposition theorem and its application to image processing
2010
Best student paper award; International audience
A novel approach for image sweeping functions using approximating scheme
2009
International audience; Using Kolmogorov's superposition theorem, complex N-dimensional signal can be expressed by simpler 1D functions. Precisely, Kolmogorov has demonstrated that any multivariate function can be decomposed into sums and compositions of monovariate functions, that are called inner and external functions. We present one of the most recent method of monovariate functions construction. The algorithm proposed by Igelnik approximates the monovariate functions. Different layers are constructed and superposed. A layer is constituted by a couple of internal and external functions, that realizes an approximation of the multivariate function with a given precision, which corresponds…