This covariance is nearly diagonalized by a second wavelet transform, which defines the scattering covariance.
State-of-the-art maximum entropy models for texture synthesis are built from statistics relying on image representations defined by convolutional neural networks (CNN).
On the opposite, a soft-thresholding on tight frames can reduce within-class variabilities while preserving class means.
The target measure is generated via a deterministic gradient descent algorithm, so as to match a set of statistics of the given, observed realization.
It is implemented in a deep convolutional network with a homotopy algorithm having an exponential convergence.
2 code implementations • 28 Dec 2018 • Mathieu Andreux, Tomás Angles, Georgios Exarchakis, Roberto Leonarduzzi, Gaspar Rochette, Louis Thiry, John Zarka, Stéphane Mallat, Joakim andén, Eugene Belilovsky, Joan Bruna, Vincent Lostanlen, Muawiz Chaudhary, Matthew J. Hirn, Edouard Oyallon, Sixin Zhang, Carmine Cella, Michael Eickenberg
The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications.
To approximate (interpolate) the marking function, in our baseline approach, we build a statistical regression model of the marks with respect some local point distance representation.
For wavelet filters, we show numerically that signals having sparse wavelet coefficients can be recovered from few phase harmonic correlations, which provide a compressive representation
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood.
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory.
Multiscale hierarchical convolutional networks are structured deep convolutional networks where layers are indexed by progressively higher dimensional attributes, which are learned from training data.
We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane.
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation.
Dictionary learning algorithms or supervised deep convolution networks have considerably improved the efficiency of predefined feature representations such as SIFT.
A rigid-motion scattering computes adaptive invariants along translations and rotations, with a deep convolutional network.
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification.
A general framework for solving image inverse problems is introduced in this paper.