| 26-12-2022 |
Prerequisites:
IMT2113
Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |
| 17-06-2022 |
Inverse problems and RKHS
There is a class of inverse problems with the property of being separable, that is, they are linear in some variables and non-linear in others. A problem in this class can be reformulated as a linear problem in a space of measures on a suitable set. Recently, Bernstein et al analyzed the solvability of this equivalent formulation in terms of a kernel defined on the same set. The objective of this project is to study how the Reproducing Kernel Hilbert Space (RKHS) associated to this kernel yields insight into the properties of the inverse problem. In particular, whether there exist closed subspaces on which the inverse problem is well-posed.
Keywords:
análisis matemático
Problemas Inversos
Prerequisites:
None.
Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |
| 24-01-2022 |
Atomic norm regularization with generic atoms
Atomic norm regularization consists in considering an atomic set that forms the building blocks for a class of objects of interest, to then use the Minkowski functional associated to its convex hull as a regularizer. A problem of the convex hull is masking: any atom in the interior of the hull will never be selected when reconstructing an object. In practice, this is avoided by normalizing the atoms. However, this may destroy the structure of the atomic set. In this iPre, we will study strategies to avoid masking, and we will propose a reconstruction method where each atom has a chance of being selected.
Prerequisites:
IMT2113
Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |
| 11-07-2019 |
Evolution of NAFLD from chromatography and MR spectroscopy data
One of the most common liver diseases is Non-Alcoholic Fatty Liver Disease (NAFLD). It is believed to be a manifestation of metabolic syndrome, and that the progression of the disease towards steatohepatitis (NASH) and cirrhosis manifests itself in changes in concentrations of fatty acids in the liver. This project has two objectives. First, to determine the empirical relation between chromatography and Magnetic Resonance (MR) spectroscopy data acquired from fatty acids. Second, to determine the geometric structure of the data by estimating the manifold along which they lie.
Prerequisites:
None.
Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |
| 07-12-2018 |
Deconvolution and optimal transport
One of the main properties of an optical system is its resolution. This is defined as the minimum separation between two ideal point sources so that they can be distinguished from one another when observed through the system. In practice, the diffraction of light imposes a physical limit to the resolution of the system. For a linear system, this process is typically modeled by a convolution by the Point Spread Function (PSF). For this reason, a technique that improves the resolution of the system can be interpreted as a deconvolution method. The objective of this project is to study the connection between deconvolution methods and optimal transport, and how the performance of deconvolution methods based on optimal transport compare to the state of the art. Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |