Stéphane Mallat

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Bargaining with reading habit is no need. Reading is not kind of something sold that you can take or not. It is a thing that will change your life to life better. It is the thing that will give you many things around the world and this universe, in the real world and here after. As what will be given by this a wavelet tour of signal processing 2nd edition,(More)
It is now well admitted in the computer vision literature that a multi-resolution decomposition provides a useful image representation for vision algorithms. In this paper we show that the wavelet theory recently developed by the mathematician Y. Meyer enables us to understand and model the concepts of resolution and scale. In computer vision we generally(More)
We introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of(More)
A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. We study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. We show that the evolution of wavelet local maxima across scales characterize the local shape of(More)
Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavelet transform are explained. We then prove that the local(More)
In this paper we review recent multichannel models developed in psychophysiology, computer vision, and image processing. In psychophysiology, multichannel models have been particularly successful in explaining some low-level processing in the visual cortex. The expansion of a function into several frequency channels provides a representation which is(More)
A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide(More)
This paper constructs translation invariant operators on L(Rd), which are Lipschitz continuous to the action of diffeomorphisms. A scattering propagator is a path ordered product of non-linear and non-commuting operators, each of which computes the modulus of a wavelet transform. A local integration defines a windowed scattering transform, which is proved(More)
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is(More)