Sparse component decomp Sparse component decomp osition (SCA) and its a osition (SCA) and its a pplications to EEG and pplications to EEG and fMRI fMRI XuPeng, YaoDeZhong, ChenHuaFu School of Life Science and Technology, University of Electronic Science and Technology of China
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Sparse component decomposition (SCA) and its applications to EEG and fMRI
Sparse component decomposition (SCA) and its applications to EEG and fMRI. XuPeng, YaoDeZhong, ChenHuaFu School of Life Science and Technology, University of Electronic Science and Technology of China. Contents. What is SCA? Approaches for SCA Applications. What is SCA. - PowerPoint PPT Presentation
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Sparse component decompositSparse component decomposition (SCA) and its applications tion (SCA) and its applications t
o EEG and fMRI o EEG and fMRI
XuPeng, YaoDeZhong, ChenHuaFuSchool of Life Science and Technology, University of Electronic Science and
Technology of China
ContentsContents
What is SCA?
Approaches for SCA
Applications
What is SCA
信号稀疏性的度量( Sparsity measurement)
信号的 模
信号的 模
信号分量或变换系数的下降率
0l
pl
What is SCAWhat is SCA
When a signal satisfies the above three conditions, this signal is said to be sparse or have sparse expression in the corresponding transformation domain.
What is SCAWhat is SCA
Fundamental hypothesis for SCA
there must be some transformation domai
n on which the signal expression is sparse(not strictly proved)
What is SCA
Fundamental hypothesis for SCA
When the transformation dictionary is big
enough compared with the signal size, there must be sparse expression for
signal in this transformation domain ;
What is SCAWhat is SCA
Overcomplete dictionary 过完备库中的分量不一定满足正交性,
称为原子 (atom) ; 原子个数远大于信号的维数; 在过完备库中,信号的表达是不唯一的
(Underdetermined system)
What is SCAWhat is SCA
How to select and construct overcomplete dictionary
Different overcomplete dictionary for different signal and purpose
What is SCAWhat is SCA
Overcomplete dictionary kinds
Pure overcomplete
Mixed overcomplete
Special overcomplete …….
Approaches for SCAApproaches for SCA
概率框架模型 (Probability Framework , PM. Zibulevsky , et al,2001)
最佳正交基法 (Best Orthogonal Basis,BOB.
Coifman, et al ,1992) Focuss 算法 (Gorodnitsky ,et al,1997) 拉格朗日乘子法 匹配追踪法 (Matching Pursuit,MP)