Biomedical Engineering Reference
In-Depth Information
This Eq. (
2.75
) is not exactly equal to the
L
1
-norm cost function, since the constraint
term is not equal to
j
=
1
|
but has form of
j
=
1
log
x
j
|
|
x
j
|
. Since these constraint
terms have similar properties, the solution obtained by minimizing this cost function
has a property very similar to the
L
1
-norm-regularized minimum-norm solution.
References
1. M.S. Hämäläinen, R.J. Ilmoniemi, Interpreting measured magnetic fields of the brain: estimates
of current distributions. Technical Report TKK-F-A559, Helsinki University of Technology
(1984)
2. M.S. Hämäläinen, R.J. Ilmoniemi, Interpreting magnetic fields of the brain: minimum norm
estimates. Med. Biol. Eng. Comput.
32
, 35-42 (1994)
3. J. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem.
Phys. Med. Biol.
32
, 11-22 (1987)
4. K. Uutela, M. Hämäläinen, E. Somersalo, Visualization of magnetoencephalographic data using
minimum current estimate. NeuroImage
10
, 173-180 (1999)
5. B.D. Jeffs, Maximally sparse constrained optimization for signal processing applications. Ph.D.
thesis, University of Southern California (1989)
6. K. Matsuura, Y. Okabe, Multiple current-dipole distribution reconstructed by modified selective
minimum-norm method, in
Biomag 96
, (Springer, Heidelberg, 2000), pp. 290-293
7. R. Tibshirani, Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B (Method-
ological)
58
(1), 267-288 (1996)
8. M.E. Tipping, Sparse Bayesian learning and relevance vector machine. J. Mach. Learn. Res.
1
,
211-244 (2001)