[Insight-users] polynomial fitting for fcMRI processing

[JSW]

Hi,

If you restrict yourself to polynomials, then why don't you use a 
LeastSquares fitting algorithm?
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
You can work out the cubic case and obtain a closed-form formula for the 
fit. I don't know
how the LevenbergMarquardt performance with respect to the LeastSquares 
fitting, but I guess
that LeastSquares fitting is both faster and more accurate in this case.

best,
Jeroen

Karen Guan wrote:
> Hi Luis,
>
> Thanks very much for the answer and the reference! However, after the 
> manual of itk::MultivariateLegendrePolynomial seems to suggest that 
> this function works only for 2D and 3D data. Although it's possible to 
> add one dummy dimension (eg. all zero), I'm wondering whether there's 
> a function more suitable for 1D signal.
>
> Best,
> - Karen
>
> On 6/6/07, *Luis Ibanez* <luis.ibanez at kitware.com 
> <mailto:luis.ibanez at kitware.com>> wrote:
>
>
>     Hi Karen,
>
>
>     You can use the Multivariate Legendre Polynomials,
>     and combine them with the Linear Kalman estimator,
>     or with the Levenberg-Marquard optimizer.
>
>     
> http://www.itk.org/Insight/Doxygen/html/classitk_1_1MultivariateLegendrePolynomial.html 
>
>     
> http://www.itk.org/Insight/Doxygen/html/classitk_1_1KalmanLinearEstimator.html 
>
>     
> <http://www.itk.org/Insight/Doxygen/html/classitk_1_1KalmanLinearEstimator.html> 
>
>     
> http://www.itk.org/Insight/Doxygen/html/classitk_1_1LevenbergMarquardtOptimizer.html 
>
>
>
>     In both cases you will be using the sum of squared
>     differences between your data and the polynomial,
>     as the metric to minimize.
>
>
>     Please look at the recent trail by Mathieu Malaterre
>     on this topic in the users list.
>
>
>
>         Regards,
>
>
>            Luis
>
>
>     --------------------
>     Karen Guan wrote:
>     > Dear all,
>     >
>     > I'm working on fcMRI processing, and need polynomial fitting
>     (3rd order,
>     > ax3 + bx2 + cx +d) for each time course (with about 600 time
>     points)
>     > to remove B0 fluctuation or shifting. The entire data set
>     > has 128 * 128 * 7 samples ( i.e. time courses).
>     >
>     > The questions are:
>     > 1. Is there such an algorithm in ITK (including vnl/vcl)?
>     > 2. If so, for fast processing of 1-D signal with 600 samples,
>     what are
>     > be best choices?
>     >
>     > I appreciate the help!
>     >
>     > - X.
>     >
>     >
>     >
>     >
>     
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