MS-Fr-D-48
Image restoration: new algorithms and new applications - Part II of III
For Part I, see MS-Th-E-48
For Part III, see MS-Fr-E-48

Date: August 14
Time: 13:30--15:30
Room: 212B

(Note: Click title to show the abstract.)

Organizer:
Sgallari, Fiorella (Univ. of Bologna)
Chan, Raymond (The Chinese Univ. of Hong Kong)

Abstract: The field of digital image restoration is concerned with the reconstruction or estimation of uncorrupted images from noisy, blurred ones. This blurring may be caused by optical distortions, object motion during imaging, or atmospheric turbulence. There are existing or potential applications of image restoration in many scientific and engineering fields, e.g. aerial imaging, remote sensing electron microscopy, and medical imaging. From these arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with and Mathematics has become one of the main driving forces of the modern development of image restoration.

The purpose of this mini-symposium is to gather the leading researchers in the areas of image restoration/reconstruction to present a series of talks that will expose the current state of knowledge in the algorithmic and application field.
Our goal is also to establish connections between different techniques, talk about important issues in the emerging application fields and generate novel ideas for future development.

MS-Fr-D-48-1
13:30--14:00
Krylov Subspace Methods for Constrained Image Restoration
James, Nagy (Emory Univ.)
Abstract: Iterative Krylov subspace methods play a central role in the regularization of image restoration problems. In this talk we consider hybrid schemes that can be used to effectively implement regularization, including determining regularization parameters. We also consider approaches to enforce sparsity and nonnegativite constraints, as well as approaches that can compensate for outliers, such as missing pixels.

MS-Fr-D-48-2
14:00--14:30
Restoration of Manifold-Valued Images by Half-Quadratic Minimization
Persch, Johannes (TU Kaiserslautern)
Abstract: The talk addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete Riemannian manifold. We recall the half-quadratic minimization method and adapt the algorithm to our special variational setting. We prove the convergence of the method for Hadamard spaces. Numerical examples for images with values on spheres, in the rotation group SO(3), and in the manifold of positive definite matrices demonstrate the algorithm.

MS-Fr-D-48-3
14:30--15:00
Image reconstruction and interpretation in Positron Emission Tomography for small animals (micro-PET)
Garbarino, Sara (Department of Mathematics, Univ. of Genoa)
Abstract: FDG-PET experiments involve two kinds of problems: the first one is the reconstruction of tracer distribution (a classical imaging inverse problem), and we focus on a Maximum Likelihood Estimation Maximization GATE-based algorithm for its implementation; the second problem is the quantification of descriptors of tracer kinetics (a compartmental inverse problem), and we present a novel approach for its resolution. We describe different applications utilizing nuclear data measured by a PET device for small animal models.

MS-Fr-D-48-4
15:00--15:30
Edge recovery in images from linear attenuating operators
Nikolova, Mila (CMLA, CNRS - ENS Cachan)
Abstract: We consider applications like eddy current (EC) of metallic parts where the quality of the representation of the layers in the material degrades with the deepness of the layer. The goal is to recover anomalies (cracks) in the metal. Contemporary methods provide resolution that rapidly decay with the depth. Our method improves this decay by adapting the regularization parameters to the attenuation. The improvement is limited by the noise.

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