Shift ∧ 2D Rotation Invariant Sparse Coding for Multivariate Signals

被引:39
作者
Barthelemy, Quentin [1 ]
Larue, Anthony [1 ]
Mayoue, Aurelien [1 ]
Mercier, David [1 ]
Mars, Jerome I. [2 ]
机构
[1] CEA LIST, Data Anal Tools Lab, F-91191 Gif Sur Yvette, France
[2] GIPSA Lab, F-38402 St Martin Dheres, France
关键词
Dictionary learning algorithm; handwritten data; multichannel; multivariate; online learning; orthogonal matching pursuit; rotation invariant; shift-invariant; sparse coding; trajectory characters; DICTIONARY LEARNING ALGORITHMS; LINEAR INVERSE PROBLEMS; OVERCOMPLETE DICTIONARIES; MATRIX-FACTORIZATION; MATCHING PURSUIT; APPROXIMATION; REPRESENTATIONS;
D O I
10.1109/TSP.2012.2183129
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Classical dictionary learning algorithms (DLA) allow unicomponent signals to be processed. Due to our interest in two-dimensional (2D) motion signals, we wanted to mix the two components to provide rotation invariance. So, multicomponent frameworks are examined here. In contrast to the well-known multichannel framework, a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure. Within this multivariate framework, we then present sparse coding methods: multivariate orthogonal matching pursuit (M-OMP), which provides sparse approximation for multivariate signals, and multivariate DLA (M-DLA), which empirically learns the characteristic patterns (or features) that are associated to a multivariate signals set, and combines shift-invariance and online learning. Once the multivariate dictionary is learned, any signal of this considered set can be approximated sparsely. This multivariate framework is introduced to simply present the 2D rotation invariant (2DRI) case. By studying 2D motions that are acquired in bivariate real signals, we want the decompositions to be independent of the orientation of the movement execution in the 2D space. The methods are thus specified for the 2DRI case to be robust to any rotation: 2DRI-OMP and 2DRI-DLA. Shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition. As validation, our methods are applied to 2D handwritten data to extract the elementary features of this signals set, and to provide rotation invariant decomposition.
引用
收藏
页码:1597 / 1611
页数:15
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