Xu Peng, Lei Xu, Hu Xiao, Yao Dezhong
Key laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, ChengDu, Sichuan, 610054, China.
Annu Int Conf IEEE Eng Med Biol Soc. 2009;2009:69-72. doi: 10.1109/IEMBS.2009.5335009.
l(0) norm is an effective constraint used to solve EEG inverse problem for a sparse solution. However, due to the discontinuous and un-differentiable properties, it is an open issue to solve the l(0) norm constrained problem, which is usually instead solved by using some alternative functions like l(1) norm to approximate l(0) norm. In this paper, a continuous and differentiable function having the same form as the transfer function of Butterworth low-pass filter is introduced to approximate l(0) norm constraint involved in EEG inverse problem. The new approximation based approach was compared with l(1) norm and LORETA solutions on a realistic head model using simulated sources. The preliminary results show that this alternative approximation to l(0) norm is promising for the estimation of EEG sources with sparse distribution.
l(0)范数是用于求解脑电逆问题以获得稀疏解的一种有效约束。然而，由于其不连续和不可微的性质，求解l(0)范数约束问题是一个开放问题，通常通过使用一些替代函数（如l(1)范数）来近似l(0)范数来解决。本文引入了一个与巴特沃斯低通滤波器传递函数具有相同形式的连续可微函数，以近似脑电逆问题中涉及的l(0)范数约束。在一个使用模拟源的真实头部模型上，将新的基于近似的方法与l(1)范数和LORETA解进行了比较。初步结果表明，这种对l(0)范数的替代近似对于估计具有稀疏分布的脑电源具有前景。
