电子科技大学：Sparse component decomposition（SCA）and its applications to EEG and fMRI

Sparse component decomposition (SCA) and its applications to EEG and fMRI XuPeng, Yao DeZhong, ChenHua Fu Schoolof life science and Technology, University of Electronic science and Technology of china

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

Contents ➢ What is SCA? ➢ Approaches for SCA ➢ Applications

What is sca 口信号稀疏性的度量( Sparsity measurement) 信号的模 信号的模 信号分量或变换系数的下降率

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 0 l p l

What is sca a 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 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 SCa a Fundamental hypothesis for SCA there must be some transformation domain on which the signal expression is sparse(not strictly proved

What is SCA ❑ Fundamental hypothesis for SCA ➢ there must be some transformation domain 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 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 sca Overcomplete dictionary 过完备库中的分量不一定满足正交性, 称为原子(aom) 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 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 sca o How to select and construct overcomplete dictionary Different overcomplete dictionary for different signal and purpose

What is SCA ⚫ How to select and construct overcomplete dictionary ➢ Different overcomplete dictionary for different signal and purpose

What is sca a Overcomplete dictionary kinds Pure overcomplete Mixed overcomplete Special overcomplete

What is SCA ❑ Overcomplete dictionary kinds ➢ Pure overcomplete ➢ Mixed overcomplete ➢ Special overcomplete ➢ ……

Approaches for SCA 概率框架模型( Probability Framework,PM Zibulevsky. et al. 200 >最佳正交基法( Best Orthogonal Basis, BOB Coifman, et al, 1992) Focuss算法( Gorodnitsky,eta1,1997) >拉格朗目乘子法 >匹配追踪法( Matching Pursuit,MP

Approaches 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)