Multidimensional compressed sensing and their applications

Authors
Caiafa, Cesar Federico; Cichocki, Andrzej
Publication Year
2013
Language
English
Format
article
Status
Published version
Description
Compressed Sensing (CS) comprises a set of relatively new techniques that exploit the underlying structure of data sets allowing their reconstruction from compressed versions or incomplete information. CS reconstruction algorithms are essentially non-linear, demanding heavy computation load and large storage memory, especially in the case of multidimensional signals. Excellent review papers discussing CS state-of-the-art theory and algorithms already exist in the literature which mostly consider data sets in vector forms. In this article, we give an overview of existing techniques with special focus on the treatment of multidimensional signals (tensors). We discuss recent trends that exploit the natural multidimensional structure of signals (tensors) achieving simple and efficient CS algorithms. The Kronecker structure of dictionaries is emphasized and its equivalence to the Tucker tensor decomposition is exploited allowing us to use tensor tools and models for CS. Several examples based on real world multidimensional signals are presented illustrating common problems in signal processing such as: the recovery of signals from compressed measurements for MRI signals or for hyper-spectral imaging, and the tensor completion problem (multidimensional inpainting).
Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Cichocki, Andrzej . Laboratory for Advanced Brain Signal Processing; Polonia. Research Systems Institute; Polonia
Subject
Compressed sensing
Sparse representations
Multidimensional signals
Multiway arrays
Ciencias de la Información y Bioinformática
Ciencias de la Computación e Información
CIENCIAS NATURALES Y EXACTAS
Access level
Restricted access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/4132