Scattering Representations for Recognition

This thesis addresses the problem of pattern and texture recognition from a mathematical perspective. These high level tasks require signal representations enjoying specific invariance, stability and consistency properties, which are not satisfied by linear representations. Scattering operators cascade wavelet decompositions and complex modulus, followed by a lowpass filtering. They define a non-linear representation which is locally translation invariant and Lipschitz continuous to the action of diffeomorphisms. They also define a texture representation capturing high order moments and which can be consistently estimated from few realizations. The thesis derives new mathematical properties of scattering representations and demonstrates its efficiency on pattern and texture recognition tasks. Thanks to its Lipschitz continuity to the action of diffeomorphisms, small deformations of the signal are linearized, which can be exploited in applications with a generative affine classifier yielding state-of-the-art results on handwritten digit classification. Expected scattering representations are applied on image and auditory texture datasets, showing their capacity to capture high order moments information with consistent estimators. Scattering representations are particularly efficient for the estimation and characterization of fractal parameters. A renormalization of scattering coefficients is introduced, giving a new insight on fractal description, with the ability in particular to characterize multifractal intermittency using consistent estimators.