I'm mostly interested in Signal Processing with emphasis on its interaction with physics.
I have therefore several different activities, the common denominators being signal and physics.
My main concerns today are :
- the study of networks of nonlinear systems, with main application to the neural system
- the possible positive influence of noise in nonlinear processings, with again as a main concern the neural system
- the theory of signals for complex systems (self-similarity and broken version, generalized stationarities)
- application of signal processing in physics
Networks of nonlinear systems
This part of my activities is at itS beginning from a theoretical point
of view. But i'm collaborationg since 2006 with Catherine Villard, a
physicist from Institut Néel,
Grenoble, France, on a project which aims at the study of real neural
networks which geometry is controlled. Furthermore, we want to
perfectly couple the neurons with
a measuring device called MicroElectrode Array. Ultimatly this will
provide us an experimental apparatus to study the function of
structured networks (see a poster presented at the 2006 MEA meeting).
At the moment, we validate the experiment in the study of small networks of three coupled neurons (see a poster presented in december 2007 at the TAUC symposium on neuroscience)! More information may be found in conference papers [62,69].
I came to this topic after having studying noise-enhaced processing in
some types of networks that mimicneural networks. This is described in
the following section. Now, I want to use these models to investigate
information flows in neural networks.
I've begun to work on this subject by the study of stochastic
resonance. I developped with Steeve Zozor the theory of stochastic
resonance in discrete time systems.
Stochastic resonance has a very precise meaning : it corresponds to a
synchronisation between two time scales that may co-exist in a
nonlinear system attacked by a periodic signal (first time scale) and a
noise (second time scale for some nonlinear systems, e.g. quartic
potential). The second time scale typically correspond to a mean escape
time. If we study the output of the nonlinear system, there is a
preferred noise power for which the periodic signal will be maximally
seen. Thus, if we plot for example the signal-to-noise ratio at the
first harmonic in the output as a function of the input noise power, we
obtain a bell shaped curve, indicating that here exists an optimal
noise power for the transmission of the periodical signal.
Steeve applied this to the problem of detecting a sine wave in noise.
If noise is not Gaussian, he designed ad-hoc networks of
nonlinearities, each processing the input with different parameters,
mimicking therefore stochastic resonance.A max operator selects the
best noninearity as the best detector. For Gaussian noise, the
procedure approaches the optimality of matched filtering, and for other
type of noise, performance may almost perfect (square ROC curves). In
particular case, the detection procedure can be termed noise-enhanced
detection and use explicitly the concept of stochastic resonance. But
there are other instances of noise enhanced detection that we have
You can have more information by reading a few of our papers, e.g. published papers [9,14,16,21]
From an engineering point of view, noise-enhanced processing seems to
be a no sense. Indeed adding noise to a signals to improve its
processing seems very strange. However, there are situations in which
noise is inherent in the system that process some system. This is the
case of the brain! It it well recognize now that neurons are noisy.
Indeed, the basic processes for the coupling between neurons (synaptic
couplings) are stochastic by nature. When looking at the response of a
neuron (or a neural network) to some sitmulus, it is striking to see
the stochastic variability of this response. I have then turned to the
study of noise-enhanced processing in the living system, by working on
very simple models. For example, with Steeve Zozor, we have study on
very simple models of the retina if microsaccads (micro- erratic
movements of the eyes) do provide a noise-enhanced processing (see submitted papers , conference papers [70,71]).
My main other concern at the moment is the study of pooling networks,
networks of neurons that process a same information in parallel, the
output of each being pooled to create the output of the networks. In
these networks, the neurons are noisy. Therefore, each neuron can be
view as highly non reliable processor, but the pooling creates a
reliable output. These kind of neural networks has been shown to
provide almost optimal processing of information (see Ma et. al.,
Nature Neuroscience, 2006, 9, 1432-1438). I work with M. McDonnell from
The University of South Australia and N. Stocks from Warwick University
on different aspects of these networks. Information may be found in conference papers [60,63,68].
Signals for complex systems
There is no well accepted definition of a comlex system, but some basic
ingredients are necessary for a system to be qualified as complex. The
system should be composed of many components in non trivial
interaction, it may exchange with the outside (energy or information).
Typical complex systems are as different as a sandpile or the
www. When measuring some variables in complex system, we are often
faced with signals that do not follow the usual good properties of a
signal: stationarity, mixing, Gaussianity. Often, one of the preceding
property is violated. If mixing is not present, then we are in front
with long range dependent signals. If Gaussianity is not present, we
may have signals with heavy tailed pdf. In both case, we are often
faced with power laws. One of
the more striking feature of a pure power law is the absence of any
caracteristic scale. This property is inherited from self-similarity. A
stochastic signal is self-similar if is equal to a time dilated version
of itself up to some amplitude renormalization. Equality here has to be
understood in the probability distribution sense. Mathematically,
self-similarity is well defined and well documented now. However, from
a physical perspective, strict self-similarity cannot exists, because
at least of the existence of cutoffs in the frequency domain. We say
that the symmetry obeyed by the signal (self-similarity) is broken.
I've worked on this subject (broken symmetries) in collaboration with
P. Flandrin and P. Borgnat, from ENSLyon. We have studied several
subjects, from Discrete Scale Invariance (the self-similarity is true
only for a discrete set of ratio) to generalized self-similarity using
general groups (however isomorphic to the reals with the addition).
Information may be found in published papers [18,23]. I also work on the use of random Iterated Function System for the design of fractal random signals, see [submitted 3, conference 67,72].
Application of Signal Processing in Physics
I have worked on many different applications of signal processing in physics (see published papers [10,12,13,19,25,28,30,31,32]).
In the more recent works, i collaborate with a group of
physicists on the study of the Extreme Ultra Violet solar spectrum. We
especially work with the data collected by SEE on-board TIMED, an
american satellite. Each day since 2002, SEE collects the solar
radiation in the EUV range (from about 20 to 200 nm) with a good
resolution. After some processing (calibration, elimination of
flares--solar big eruptions--), the data are in form of a spectrum,
composed of the emission lines of many elements (and different
configuration of each) present in the Sun. Further, the variability of
the Sun is then reflected by the daily measurement of this spectrum. We
have applied on these data a Bayesian approach to source separation nly
imposing the constraint of positivity of the sources (indeed, they are
spectra). With such a approach we are able to separate the solar EUV
specrtum into the superposition of 3 spectra which are physically
interpretable (see submitted paper ).