@inproceedings{Luengo2013,
title = {Cross-Products LASSO},
author = {David Luengo and Javier Via and Sandra Monzon and Tom Trigano and Antonio Artés-Rodríguez},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6638840},
issn = {1520-6149},
year = {2013},
date = {2013-01-01},
booktitle = {2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
pages = {6118--6122},
publisher = {IEEE},
address = {Vancouver},
abstract = {Negative co-occurrence is a common phenomenon in many signal processing applications. In some cases the signals involved are sparse, and this information can be exploited to recover them. In this paper, we present a sparse learning approach that explicitly takes into account negative co-occurrence. This is achieved by adding a novel penalty term to the LASSO cost function based on the cross-products between the reconstruction coefficients. Although the resulting optimization problem is non-convex, we develop a new and efficient method for solving it based on successive convex approximations. Results on synthetic data, for both complete and overcomplete dictionaries, are provided to validate the proposed approach.},
keywords = {Approximation methods, approximation theory, concave programming, convex programming, Cost function, cross-product LASSO cost function, Dictionaries, dictionary, Encoding, LASSO, learning (artificial intelligence), negative co-occurrence, negative cooccurrence phenomenon, nonconvex optimization problem, Signal processing, signal processing application, signal reconstruction, sparse coding, sparse learning approach, Sparse matrices, sparsity-aware learning, successive convex approximation, Vectors},
pubstate = {published},
tppubtype = {inproceedings}
}

Negative co-occurrence is a common phenomenon in many signal processing applications. In some cases the signals involved are sparse, and this information can be exploited to recover them. In this paper, we present a sparse learning approach that explicitly takes into account negative co-occurrence. This is achieved by adding a novel penalty term to the LASSO cost function based on the cross-products between the reconstruction coefficients. Although the resulting optimization problem is non-convex, we develop a new and efficient method for solving it based on successive convex approximations. Results on synthetic data, for both complete and overcomplete dictionaries, are provided to validate the proposed approach.

@inproceedings{Montoya-Martinez2012,
title = {Structured Sparsity Regularization Approach to the EEG Inverse Problem},
author = {Jair Montoya-Martinez and Antonio Artés-Rodríguez and Lars Kai Hansen and Massimiliano Pontil},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6232898},
isbn = {978-1-4673-1878-5},
year = {2012},
date = {2012-01-01},
booktitle = {2012 3rd International Workshop on Cognitive Information Processing (CIP)},
pages = {1--6},
publisher = {IEEE},
address = {Baiona},
abstract = {Localization of brain activity involves solving the EEG inverse problem, which is an undetermined ill-posed problem. We propose a novel approach consisting in estimating, using structured sparsity regularization techniques, the Brain Electrical Sources (BES) matrix directly in the spatio-temporal source space. We use proximal splitting optimization methods, which are efficient optimization techniques, with good convergence rates and with the ability to handle large nonsmooth convex problems, which is the typical scenario in the EEG inverse problem. We have evaluated our approach under a simulated scenario, consisting in estimating a synthetic BES matrix with 5124 sources. We report results using ℓ1 (LASSO), ℓ1/ℓ2 (Group LASSO) and ℓ1 + ℓ1/ℓ2 (Sparse Group LASSO) regularizers.},
keywords = {BES, brain electrical sources matrix, Brain modeling, EEG inverse problem, Electrodes, Electroencephalography, good convergence, Inverse problems, large nonsmooth convex problems, medical signal processing, optimisation, Optimization, proximal splitting optimization methods, Sparse matrices, spatio-temporal source space, structured sparsity regularization approach, undetermined ill-posed problem},
pubstate = {published},
tppubtype = {inproceedings}
}

Localization of brain activity involves solving the EEG inverse problem, which is an undetermined ill-posed problem. We propose a novel approach consisting in estimating, using structured sparsity regularization techniques, the Brain Electrical Sources (BES) matrix directly in the spatio-temporal source space. We use proximal splitting optimization methods, which are efficient optimization techniques, with good convergence rates and with the ability to handle large nonsmooth convex problems, which is the typical scenario in the EEG inverse problem. We have evaluated our approach under a simulated scenario, consisting in estimating a synthetic BES matrix with 5124 sources. We report results using ℓ1 (LASSO), ℓ1/ℓ2 (Group LASSO) and ℓ1 + ℓ1/ℓ2 (Sparse Group LASSO) regularizers.

@inproceedings{Vinuelas-Peris2009,
title = {Sensing Matrix Optimization in Distributed Compressed Sensing},
author = {Pablo Vinuelas-Peris and Antonio Artés-Rodríguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278496},
isbn = {978-1-4244-2709-3},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
pages = {638--641},
publisher = {IEEE},
address = {Cardiff},
abstract = {Distributed compressed sensing (DCS) seeks to simultaneously measure signals that are each individually sparse in some domain(s) and also mutually correlated. In this paper we consider the scenario in which the (overcomplete) bases for common component and innovations are different. We propose and analyze a distributed coding strategy for the common component, and also the use of efficient projection (EP) method for optimizing the sensing matrices in this setting. We show the effectiveness of our approach by computer simulations using the orthogonal matching pursuit (OMP) as joint recovery method, and we discuss the configuration of the distribution strategy.},
keywords = {Compressed sensing, Computer Simulation, computer simulations, correlated signal, Correlated signals, correlation theory, Dictionaries, distributed coding strategy, distributed compressed sensing, Distributed control, efficient projection method, Encoding, joint recovery method, Matching pursuit algorithms, Optimization methods, orthogonal matching pursuit, Projection Matrix Optimization, sensing matrix optimization, Sensor Network, Sensor phenomena and characterization, Sensor systems, Signal processing, Sparse matrices, Technological innovation},
pubstate = {published},
tppubtype = {inproceedings}
}

Distributed compressed sensing (DCS) seeks to simultaneously measure signals that are each individually sparse in some domain(s) and also mutually correlated. In this paper we consider the scenario in which the (overcomplete) bases for common component and innovations are different. We propose and analyze a distributed coding strategy for the common component, and also the use of efficient projection (EP) method for optimizing the sensing matrices in this setting. We show the effectiveness of our approach by computer simulations using the orthogonal matching pursuit (OMP) as joint recovery method, and we discuss the configuration of the distribution strategy.