Holistic Sensing, Estimating and Processing of Random Fields with Sensor Arrays.
Event details
| Date | 18.07.2016 |
| Hour | 09:30 › 11:30 |
| Speaker | Matthieu Simeoni |
| Location | |
| Category | Conferences - Seminars |
EDIC Candidacy Exam
Exam President: Prof. Michael Unser
Thesis Director: Prof. Martin Vetterli
Thesis Co-director: Prof. Victor Panaretos
Co-examiner: Prof. Patrick Thiran
Background papers:
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular
domains, by Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. Signal Processing Magazine IEEE, 30(3), 83-98.
Sparse sampling of signal innovations, by Blu, T., Dragotti, P. L., Vetterli, M., Marziliano, P., & Coulot, L. Signal Processing Magazine, IEEE, 25(2), 31-40.
Methodology and convergence rates for functional linear regression. The Annals of Statistics, 35(1), 70-91.
Abstract
Many scientific applications involve estimating the sufficient statistics of a physical phenomenon modelled as a continuous random
field. In practice, data is collected through an acquisition system, typically a sensor array, consisting in a very large network of
sensors, filtering and sampling the incoming field at different locations. Recently, hierarchical designs have been proposed for these
arrays, where groups of sensors are beamformed together so as to modify the properties of the spatial filtering performed by the
array. Mathematically speaking, this acquisition system can be conveniently interpreted as a sampling operator, chain of linear
operators acting subsequently on the random field (filtering, sampling, beamforming, etc). Formulating the problem in such general
terms permits to bring it into the scope of a variety of different methods, such as Functional Data Analysis, Finite Rate of Innovation or
Graph Signal Processing. In this thesis, we adopt an holistic view on the system, and propose inter-linked algorithms for each of the
individual steps of the data processing pipeline, including, but not restricted to: a versatile beamforming strategy to achieve a
wide-range of spatial filters; a resolution-free least-squares estimation procedure based on functional linear regression; and finally an
algorithm for extracting relevant features of the random field. For each of the proposed algorithms and unlike state of the art methods,
we work as much as possible at the analytical level, considering the unknowns as continuous objects in some infinite-dimensional
Hilbert space. Discretisation is pushed to the very end of the processing chain, for the sole purpose of visualisation. We forecast that
such an approach will lead to tremendous improvements over state of the art methods in terms of accuracy, numerical stability,
memory storage and computational resources.
Exam President: Prof. Michael Unser
Thesis Director: Prof. Martin Vetterli
Thesis Co-director: Prof. Victor Panaretos
Co-examiner: Prof. Patrick Thiran
Background papers:
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular
domains, by Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. Signal Processing Magazine IEEE, 30(3), 83-98.
Sparse sampling of signal innovations, by Blu, T., Dragotti, P. L., Vetterli, M., Marziliano, P., & Coulot, L. Signal Processing Magazine, IEEE, 25(2), 31-40.
Methodology and convergence rates for functional linear regression. The Annals of Statistics, 35(1), 70-91.
Abstract
Many scientific applications involve estimating the sufficient statistics of a physical phenomenon modelled as a continuous random
field. In practice, data is collected through an acquisition system, typically a sensor array, consisting in a very large network of
sensors, filtering and sampling the incoming field at different locations. Recently, hierarchical designs have been proposed for these
arrays, where groups of sensors are beamformed together so as to modify the properties of the spatial filtering performed by the
array. Mathematically speaking, this acquisition system can be conveniently interpreted as a sampling operator, chain of linear
operators acting subsequently on the random field (filtering, sampling, beamforming, etc). Formulating the problem in such general
terms permits to bring it into the scope of a variety of different methods, such as Functional Data Analysis, Finite Rate of Innovation or
Graph Signal Processing. In this thesis, we adopt an holistic view on the system, and propose inter-linked algorithms for each of the
individual steps of the data processing pipeline, including, but not restricted to: a versatile beamforming strategy to achieve a
wide-range of spatial filters; a resolution-free least-squares estimation procedure based on functional linear regression; and finally an
algorithm for extracting relevant features of the random field. For each of the proposed algorithms and unlike state of the art methods,
we work as much as possible at the analytical level, considering the unknowns as continuous objects in some infinite-dimensional
Hilbert space. Discretisation is pushed to the very end of the processing chain, for the sole purpose of visualisation. We forecast that
such an approach will lead to tremendous improvements over state of the art methods in terms of accuracy, numerical stability,
memory storage and computational resources.
Practical information
- General public
- Free
Contact
- Cecilia Chapuis EDIC