Results 1 
6 of
6
Minimum Mean Square Distance Estimation of a Subspace IRIT/ENSEEIHT, 2011 [Online]. Available: http://dobigeon.perso.enseeiht.fr/app_MMSD.html
"... Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natur ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natural metric in the Grassmann manifold GN;p, i.e., the set of pdimensional subspaces in N. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UU T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative
Differential Feedback of MIMO Channel Gram Matrices Based on Geodesic Curves
"... Abstract—This paper proposes a differential quantization strategy to be used in the feedback link of a multipleinput multipleoutput (MIMO) communication system. This algorithm is applied to the channel Gram matrix using geodesic curves and exploiting the intrinsic geometry of positive definite Her ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Abstract—This paper proposes a differential quantization strategy to be used in the feedback link of a multipleinput multipleoutput (MIMO) communication system. This algorithm is applied to the channel Gram matrix using geodesic curves and exploiting the intrinsic geometry of positive definite Hermitian matrices. It also exploits the temporal correlation of the channel, and follows on average the gradient of the cost function associated to the transmitter design criterion. A full description of the algorithm, including the computational cost and a numerical analysis of the effect of delays and errors in the feedback link is presented. Simulation results show that the proposed algorithm improves other techniques based on the direct quantization of the channel response matrix or the quantization of the subspace spanned by the strongest eigenmodes of the MIMO channel, i.e., Grassmannian based techniques. The main drawback of Grassmannian based algorithms is that the transmitter is constrained to apply a uniform power allocation among spatial transmission modes, which is not forced in the algorithm proposed in this paper. Index Terms—MIMO systems, quantization, differential geometry, feedback communication, feedback delay, feedback errors,
Covariance Descriptors for 3D Shape Matching and Retrieval
"... Several descriptors have been proposed in the past for 3D shape analysis, yet none of them achieves best performance on all shape classes. In this paper we propose a novel method for 3D shape analysis using the covariance matrices of the descriptors rather than the descriptors themselves. Covarian ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Several descriptors have been proposed in the past for 3D shape analysis, yet none of them achieves best performance on all shape classes. In this paper we propose a novel method for 3D shape analysis using the covariance matrices of the descriptors rather than the descriptors themselves. Covariance matrices enable efficient fusion of different types of features and modalities. They capture, using the same representation, not only the geometric and the spatial properties of a shape region but also the correlation of these properties within the region. Covariance matrices, however, lie on the manifold of Symmetric Positive Definite (SPD) tensors, a special type of Riemannian manifolds, which makes comparison and clustering of such matrices challenging. In this paper we study covariance matrices in their native space and make use of geodesic distances on the manifold as a dissimilarity measure. We demonstrate the performance of this metric on 3D face matching and recognition tasks. We then generalize the Bag of Features paradigm, originally designed in Euclidean spaces, to the Riemannian manifold of SPD matrices. We propose a new clustering procedure that takes into account the geometry of the Riemannian manifold. We evaluate the performance of the proposed Bag of Covariance Matrices framework on 3D shape matching and retrieval applications and demonstrate its superiority compared to descriptorbased techniques. 1.
SPECTRUM LABELING FOR COGNITIVE RADIO SYSTEMS: CANDIDATE SPECTRAL ESTIMATION
"... A key challenge of the air interface of the cognitive radio is an accurate detection of weak signals of licensed users over a wide spectrum range. This paper describes a method for first detecting and next locating in frequency a given primary user, even when a noncandidate interference is located ..."
Abstract
 Add to MetaCart
(Show Context)
A key challenge of the air interface of the cognitive radio is an accurate detection of weak signals of licensed users over a wide spectrum range. This paper describes a method for first detecting and next locating in frequency a given primary user, even when a noncandidate interference is located at the same frequency. The range of SNR that is covered proves that the estimate is efficient for realistic scenarios. In addition, the good performance is kept even for very short data records (50 symbols of the candidate signal). The proposed technique shows much better performance than energy detectors and less complexity than cyclostationary based ones. Index Terms — Cognitive radio, spectrum sensing, spectrum analysis.
des canaux à antennes multiples ENST ParisMotorola Labs Saclay
"... A mes parents Pour l’amour, l’encouragement et l’éducation qu’ils ont su me donner A mon mari Pour les sacrifices, pour l’amour, le soutien, l’encouragement, l’aide qu’il a su m’apporter A mon bébé Pour tout le bonheur qu’il m’a offert. Remerciements ..."
Abstract
 Add to MetaCart
(Show Context)
A mes parents Pour l’amour, l’encouragement et l’éducation qu’ils ont su me donner A mon mari Pour les sacrifices, pour l’amour, le soutien, l’encouragement, l’aide qu’il a su m’apporter A mon bébé Pour tout le bonheur qu’il m’a offert. Remerciements