Efficient Regularization of High-Dimensional Inverse Problems for Data Processing
ANR GRANT “JCJC” (young researcher) 2021-2024
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About EFFIREG…
Objective: Design efficient data processing algorithms in a mathematically founded way using the theory of inverse problems and low-dimensional models.
Summary: The need to efficiently process large amount of data has become ubiquitous, be it for real-time video processing on mobile device, optimization of medical imaging techniques with cost constraints or pattern recognition on large databases. Examples of such processing tasks are denoising of high-definition videos in low light conditions and magnetic resonance imaging (MRI) of the brain. Other typical processes from signal processing include interpolation (increase the resolution of a digital image) or removing blur on an image. Using the variational formulation of high dimensional inverse problems, we formalize the notion of efficient estimation method for a large class of inverse problems in data processing and we propose ways to look for the best methods and algorithms possible to solve a given problem, in a mathematically founded way. The project proposes to link the theoretical questions to applications in medical imaging where the dimensionality and quantity of data require efficient processing methods. By its scope that goes from theoretical mathematical questions to practical questions, this project has the ambition to advance the way data processing methods are designed and apply these new methodologies to the concrete impactful application of medical imaging.
Publications:
See on my publications page.
Project team:
- Yann Traonmilin (PI), CNRS researcher, Institut de mathématiques de Bordeaux
- Jean-François Aujol, Professor U. Bordeaux, Institut de mathématiques de Bordeaux
- Arthur Leclaire, Associate professor U. Bordeaux, Institut de mathématiques de Bordeaux
- Baudouin Denis de Senneville, CNRS research director, Institut de mathématiques de Bordeaux
- Samuel Vaiter, CNRS researcher, Institut de mathématiques de Bourgogne
- Pierre-Jean Bénard, PhD Student, Institut de mathématiques de Bordeaux
- Hui Shi, PhD Student, Institut de mathématiques de Bordeaux
Codes:
Sketching for image denoising. H. Shi
Fast projected gradient descent. PJ Bénard