Computer Science Colloquium
From Scattering to Spectral Networks
Joan Bruna, CIMS
May 02, 2014
Warren Weaver Hall, 1302
251 Mercer Street
New York, NY 10012
Spring 2014 Colloquia Calendar
Object and Texture Classification are fundamental problems in which one is required
to extract stable, discriminative information out of noisy, high-dimensional signals.
Our perception of image and audio patterns is invariant under several transformations,
such as illumination changes, translations or frequency transpositions, as well as
small geometrical perturbations. Similarly, textures are examples of stationary,
non-gaussian, intermittent processes which can be recognized from few realizations.
Scattering operators construct a non-linear signal representation
by cascading wavelet modulus decompositions, shown to be
stable to geometric deformations, and capturing high-order moments
with low-variance estimators. Moreover, scattering coefficients encode the presence
of geometric regularity, modulation phenomena, intermittency and self-similarity,
leading to efficient classification, detection and characterization of several pattern and
multifractal texture recognition tasks.
Although stability to geometric perturbations is necessary, it is not sufficient
for the most challenging object recognition tasks, which require learning
the invariance from data. We shall see that scattering operators
can be generalized to this scenario, highlighting the close links between
structured dictionary learning approaches and deep neural networks.
Joan Bruna graduated from Universitat Politècnica de Catalunya in both
Mathematics and Electrical Engineering, in 2002 and 2004
respectively. He obtained an MSc in applied
mathematics from ENS Cachan in 2005. From
2005 to 2012, he was a research engineer in an
image processing startup, developing realtime
video processing algorithms resulting in a dozen international patents.
In 2013 he obtained his PhD in Applied Mathematics at École
Polytechnique, under the supervision of Prof. Stéphane Mallat.
Since fall 2012 he is a postdoctoral researcher in Yann LeCun's
lab at the Courant Institute, New York. His research interests include
invariant signal representations,
stochastic processes, harmonic analysis, deep learning, and
its applications to computer vision.