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Contenido archivado el 2024-05-29

Sparse approximations for blind source separation

Objetivo

The project will focus on novel mathematical, numerical, and algorithmic tools for Blind Source Separation (BSS) and on innovative applications in digital signal and image restoration. In nature several observed phenomena are a suitable superposition of basic sources. To understand the core of such phenomena and their origin it is fundamental to separate such contributions. Within this general framework several analyses and methods have been proposed.

One of the most successful is the Independent Component Analysis (ICA), where the source is assumed to be a vector valued signal with component as statistically independent as possible. Nevertheless ICA cannot be a universal tool for any BSS problem. In fact in several concrete applications the independence assumption is unrealistic. The project will investigate a new generation of methods for BSS based on the so-called sparsity assumption: The source signal components are assumed to be represented as a sum of weighted basic signals belonging to a prescribed dictionary where only few of them are relevant.

Typically one can think that the signals belong to a certain Banach space of functions and that the dictionary is an unconditional basis or a frame for this space. Since the sparsity assumption depends on the dictionary, one can also design the dictionary in order to obtain the sparsest representation. Also for this reason, the sparsity assumption is often more realistic than the sole statistical independence. We will provide the mathematical framework for BSS based on sparisity assumptions, together with numerical and algorithmic tools for its solution. We will focus on specific applications in image processing and in particular for functional Magnetic Resonance Imaging (fMRI).

Ámbito científico (EuroSciVoc)

Palabras clave

Tema(s)

Convocatoria de propuestas

FP6-2005-MOBILITY-6
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Régimen de financiación

OIF - Marie Curie actions-Outgoing International Fellowships

Coordinador

AUSTRIAN ACADEMY OF SCIENCES (OESTERREICHISCHE AKADEMIE DER WISSENSCHAFTEN)
Aportación de la UE
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Coste total
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Participantes (1)