| 21-11-2023 |
Inversión del problema de pronóstico de tiempo de descarga de baterías con Deep Reinforcement Learning
El tiempo en que ocurre la descarga de una batería en el futuro depende de cuál es la energía actual almacenada y cómo se dispondrá de ella posteriormente, es decir, de cómo se descargará la batería en el futuro. En esta investigación se busca invertir este problema. La idea principal es definir el tiempo futuro en que se desea se descargue una batería, y con esa información construir una función que defina cómo ha de descargarse la batería para conseguir tal propósito. Esta función corresponde a una red neuronal profunda, la cual es entrenada mediante aprendizaje reforzado. Este trabajo contempla reuniones semanales para reporte de avances y discusión. Ya se cuenta con un código base en Python, y la idea principal es afinar resultados y explorar mejoras.
Prerequisitos:
no tiene.
Tiene un método de evaluación Nota 1-7, con 10 créditos y tiene 1/2 vacantes disponibles |
Mentor(es): Ver en la plataforma |
| 20-12-2020 |
Biopsia Virtual con Resonancia Magnética (MRI) Cardíaca y Aprendizaje Profundo
MRI es una poderosa tecnología para el diagnóstico y seguimiento no-invasivo de varias enfermedades. Magnetic Resonance Fingerprinting (MRF) se ha propuesto para caracterizar múltiples parámetros de los tejidos en una sola adquisición, de modo que los médicos puedan utilizar esos parámetros como una "biopsia virtual". MRF se basa en: 1) el diseño de secuencias de adquisición basada en la física de MRI, 2) generación de diccionarios para describir la evolución de la señal de MRI, 3) reconstrucción a partir de datos submuestreados como un problema inverso, y la 4) concordancia de patrones entre las huellas digitales de MRF y la señal medida. Esta investigación incluye el desarrollo de novedosas secuencias de MRI, técnicas de reconstrucción de imágenes a partir de datos submuestreos, corrección de movimiento y métodos de deep learning para los diferentes pasos de MRF cardíaca. Dependiendo del proyecto sería útil saber fundamentos de MRI o AI.
Prerequisitos:
no tiene.
Tiene un método de evaluación Nota 1-7, con 10 créditos y tiene 9/10 vacantes disponibles |
Mentor(es): Ver en la plataforma |
| 21-11-2023 |
Prerequisites:
None.
Evaluation method: Nota 1-7, with 1/2 available vacants |
Mentor(s): Open in the plataform |
| 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 |
| 08-04-2021 |
Mathematical methods for the deconvolution problem
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 mathematical methods proposed in the literature in the past decade, which combine applied Fourier analysis, convex optimization, and probability, for which there exists conditions that ensure they solve the superresolution problem in a computationally efficient manner.
Prerequisites:
IMT2113
Evaluation method: Nota 1-7, with 0/1 available vacants |
Mentor(s): Open in the plataform |
| 20-12-2020 |
Virtual Biopsy with Cardiac Magnetic Resonance Fingerprinting and Deep Learning
Magnetic Resonance Imaging (MRI) is a powerful non-invasive medical image tool which is used for the diagnosis and treatment follow up of several diseases. MR Fingerprinting (MRF) has been recently proposed to characterize multiple tissue parameters in a single time-efficient scan, so these parameters can be used by clinicians as a “virtual biopsy”. MRF relies on: 1) MRI physics-based sequence design, 2) dictionary generation to describe the MRI signal evolution, 3) reconstruction from undersampled data as an inverse problem, and 4) pattern matching between the fingerprints and the measured signal. Additionally motion correction techniques are required in the case of imaging the heart, due to cardiac and respiration motion. This research includes the development of novel MR sequences, undersampled reconstruction techniques, motion compensation and deep learning approaches for the different steps of cardiac MRF. Depending on the project it would be useful to know about the fundamentals of MRI, optimization or AI.
Prerequisites:
None.
Evaluation method: Nota 1-7, with 9/10 available vacants |
Mentor(s): Open in the plataform |