6:15 PM - 7:30 PM
[SEM33-P08] The 3-D magnetic imaging using the L-1 norm regularization, Part II.
Keywords:L1 regularization, magnetc inversion, aeromagnetic survey
Lasso (Tibshirani, 1996) is a linear regression and variable selection procedure based on the L1 penalized least square. L1 penalty has an effect of shrinkage the value of model parameters which have weak contributions to be zero. So, the Lasso does both continuous shrinkage and automatic variable selection simultaneously. On the other hand, Lasso has some drawbacks. One of them is, at most Lasso algorithm can select nonzero variables of same number of observed data. So, in the case of p << n problem, i.e. when the number of unknown parameters (n) is larger than the number of observations (p), this algorithm cannot be adopted or overly shrinkage model will be obtained.
To overcome this limitation, Zou and Hastie (2005) proposed a new L-1 penalized method named 'elastic net', and Hebiri and van de Geer (2011) proposed 'S-Lasso'. These methods are the compromise of the L-1 and L-2 or some quadratic regularization method. Using these methods, we can treat p << n problems in the framework of L-1 penalized method.
In This study, we propose a new 3-D magnetic inversion method based on the Lasso-type regularization (i.e. generalized elastic net) and show the results of applying our method to the synthesized and real magnetic data.