TY - GEN
T1 - Tensor sparse coding for region covariances
AU - Sivalingam, Ravishankar
AU - Boley, Daniel
AU - Morellas, Vassilios
AU - Papanikolopoulos, Nikolaos
PY - 2010
Y1 - 2010
N2 - Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher-order data like images are usually vectorized before processing. However, the structure of the data may be lost in the process, leading to poor representation and overall performance degradation. In this paper we propose a novel approach for sparse representation of positive definite matrices, where vectorization would have destroyed the inherent structure of the data. The sparse decomposition of a positive definite matrix is formulated as a convex optimization problem, which falls under the category of determinant maximization (MAXDET) problems [1], for which efficient interior point algorithms exist. Experimental results are shown with simulated examples as well as in real-world computer vision applications, demonstrating the suitability of the new model. This forms the first step toward extending the cornucopia of sparsity-based algorithms to positive definite matrices.
AB - Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher-order data like images are usually vectorized before processing. However, the structure of the data may be lost in the process, leading to poor representation and overall performance degradation. In this paper we propose a novel approach for sparse representation of positive definite matrices, where vectorization would have destroyed the inherent structure of the data. The sparse decomposition of a positive definite matrix is formulated as a convex optimization problem, which falls under the category of determinant maximization (MAXDET) problems [1], for which efficient interior point algorithms exist. Experimental results are shown with simulated examples as well as in real-world computer vision applications, demonstrating the suitability of the new model. This forms the first step toward extending the cornucopia of sparsity-based algorithms to positive definite matrices.
KW - MAXDET optimization
KW - Positive definite matrices
KW - region covariances
KW - sparse coding
UR - http://www.scopus.com/inward/record.url?scp=78149295108&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78149295108&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-15561-1_52
DO - 10.1007/978-3-642-15561-1_52
M3 - Conference contribution
AN - SCOPUS:78149295108
SN - 364215560X
SN - 9783642155604
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 722
EP - 735
BT - Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings
PB - Springer Verlag
T2 - 11th European Conference on Computer Vision, ECCV 2010
Y2 - 10 September 2010 through 11 September 2010
ER -