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Research talks;Analysis and its Applications;Mathematics in Science and Technology

In this talk, we investigate in a unified way the structural properties of a large class of convex regularizers for linear inverse problems. These penalty functionals are crucial to force the regularized solution to conform to some notion of simplicity/low complexity. Classical priors of this kind includes sparsity, piecewise regularity and low-rank. These are natural assumptions for many applications, ranging from medical imaging to machine learning.
imaging - image processing - sparsity - convex optimization - inverse problem - super-resolution
In this talk, we investigate in a unified way the structural properties of a large class of convex regularizers for linear inverse problems. These penalty functionals are crucial to force the regularized solution to conform to some notion of simplicity/low complexity. Classical priors of this kind includes sparsity, piecewise regularity and low-rank. These are natural assumptions for many applications, ranging from medical imaging to machine ...

62H35 ; 65D18 ; 94A08 ; 68U10 ; 90C31 ; 80M50 ; 47N10

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Research schools

Can modern signal processing be used to overcome the diffraction limit? The classical diffraction limit states that the resolution of a linear imaging system is fundamentally limited by one half of the wavelength of light. This implies that conventional light microscopes cannot distinguish two objects placed within a distance closer than 0.5 × 400 = 200nm (blue) or 0.5 × 700 = 350nm (red). This significantly impedes biomedical discovery by restricting our ability to observe biological structure and processes smaller than 100nm. Recent progress in sparsity-driven signal processing has created a powerful paradigm for increasing both the resolution and overall quality of imaging by promoting model-based image acquisition and reconstruction. This has led to multiple influential results demonstrating super-resolution in practical imaging systems. To date, however, the vast majority of work in signal processing has neglected the fundamental nonlinearity of the object-light interaction and its potential to lead to resolution enhancement. As a result, modern theory heavily focuses on linear measurement models that are truly effective only when object-light interactions are weak. Without a solid signal processing foundation for understanding such nonlinear interactions, we undervalue their impact on information transfer in the image formation. This ultimately limits our capability to image a large class of objects, such as biological tissue, that generally are in large-volumes and interact strongly and nonlinearly with light.
The goal of this talk is to present the recent progress in model-based imaging under multiple scattering. We will discuss several key applications including optical diffraction tomography, Fourier Ptychography, and large-scale Holographic microscopy. We will show that all these application can benefit from models, such as the Rytov approximation and beam propagation method, that take light scattering into account. We will discuss the integration of such models into the state-of-the-art optimization algorithms such as FISTA and ADMM. Finally, we will describe the most recent work that uses learned-priors for improving the quality of image reconstruction under multiple scattering.
Can modern signal processing be used to overcome the diffraction limit? The classical diffraction limit states that the resolution of a linear imaging system is fundamentally limited by one half of the wavelength of light. This implies that conventional light microscopes cannot distinguish two objects placed within a distance closer than 0.5 × 400 = 200nm (blue) or 0.5 × 700 = 350nm (red). This significantly impedes biomedical discovery by ...

94A12 ; 94A08 ; 65T50 ; 65N21 ; 65K10 ; 62H35

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- viii; 122 p.
ISBN 978-3-642-19579-2

Lecture notes in mathematics , 2019

Localisation : Collection 1er étage

probabilité géométrique # complexité topologique # fonction aléatoire # champ aléatoire gaussien

60-02 ; 60G15 ; 55N35 ; 60Gxx ; 60G60 ; 53Cxx ; 62H35 ; 60G55 ; 53C65 ; 60-01 ; 60D05

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- 309 p.
ISBN 978-0-387-95547-6

Applied mathematical sciences , 0155

Localisation : Ouvrage RdC (CHAL)

traitement d'image # modélisation stochastique # statistique # chaîne de Markov # analyse d'image # modèle de spline # estimation paramétrique # optimisation stochastique # champs gaussien continu

68U10 ; 00A71 ; 62-02 ; 62H35 ; 62M40 ; 65C40 ; 68-02 ; 90C90

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- xvi; 387 p.
ISBN 978-3-540-44213-4

Applications of mathematics , 0027

Localisation : Ouvrage RdC (WINK)

analyse d'images # champ aléatoire # méthode de Monte Carlo # traitement d'image # simulation # échantillonage # chaîne de Markov # algorithme de Metropolis # texture # réseau de neurones # tomographie # estimation de paramètres

62H35 ; 62M40 ; 68U20 ; 65C05 ; 65C40 ; 65Y05 ; 60J20 ; 60K35 ; 68U10 ; 68-02 ; 65K10 ; 93E10

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- xii; 273 p.
ISBN 978-0-387-72635-9

Interdisciplinary applied mathematics , 0034

Localisation : Ouvrage RdC (DESO)

géométrie stochastique # théorie de la Gestalt # analyse d'images # traitement d'image # tomographie # vision assistée par ordinateur # géométrie stochastique # probabilités

62H35 ; 68T45 ; 68U10 ; 94A08 ; 62G32 ; 68-02 ; 92C55

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- xi, 257 p.
ISBN 978-3-540-68480-0

Lecture notes in mathematics , 1948

Localisation : Collection 1er étage

reconnaissance de forme # méthode a contrario # méthode de sélection des lignes de niveau # algorithme SIFT # regroupement de formes # analyse d'image # inférence non paramétrique # base de données

62C05 ; 62G10 ; 62G32 ; 62H11 ; 62H15 ; 62H30 ; 62H35 ; 68T10 ; 68T45 ; 68U10 ; 94A08 ; 94A13 ; 94B70

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