Perform the adaptive weights smoothing procedure
fmri.smooth(spm, hmax = 4, adaptation="aws",
lkern="Gaussian", skern="Plateau", weighted=TRUE,...)object with class attributes "fmrispm" and "fmridata", or "fmrisegment" and "fmridata" for segmentation choice
smoothed parameter estimate
variance of the parameter
maximum bandwidth used
smoothness in resel space. all directions
smoothness in resel space as would be achieved by a Gaussian filter with the same bandwidth. all directions
array of spatial correlations with maximal lags 5, 5, 3 in x,y and z-direction.
vector of bandwidths (in FWHM) corresponding to the spatial correlation within the data.
dimension of the data cube and residuals
ratio of voxel dimensions
ratio of estimated variances for the stimuli given by
vvector
Expected BOLD response for the specified effect
object of class fmrispm
maximum bandwidth to smooth
character, type of adaptation. If "none" adaptation is off and non-adaptive
kernel smoothing with lkern and bandwidth hmax is used.
Other values are "aws" for adaptive smoothing using an approximative correction term for spatial smoothness in the penalty (fast), "fullaws" for adaptive smoothing using variance
estimates from smoothed residuals in the penalty (CPU-time about twice
the time compared to adaptation="aws" and "segment" for a
new approach based on segmentation using multi-scale tests.
lkern specifies the location kernel. Defaults to
"Gaussian", other choices are "Triangle" and "Plateau". Note that the location kernel is applied to
(x-x_j)^2/h^2, i.e. the use of "Triangle" corresponds to the
Epanechnicov kernel in nonparametric kernel regression. "Plateau" specifies a kernel that is equal to 1 in the interval (0,.3),
decays linearly in (.5,1) and is 0 for arguments larger than 1.
skern specifies the kernel for the statistical
penalty. Defaults to "Plateau", the alternatives are "Triangle" and "Exp".
"Plateau" specifies a kernel that is equal to 1 in the interval (0,.3),
decays linearly in (.3,1) and is 0 for arguments larger than 1.
lkern="Plateau" and lkern="Triangle" allow for much faster computation (saves up
to 50% CPU-time). lkern="Plateau" produces a less random weighting scheme.
weighted (logical) determines if weights contain the inverse of local
variances as a factor (Weighted Least Squares). weighted=FALSE does not employ the
heteroscedasticity of variances for the weighting scheme and is preferable if variance estimates
are highly variable, e.g. for short time series.
Further internal arguments for the smoothing algorithm usually not
to be set by the user. Allows e.g. for parameter adjustments by
simulation using our propagation condition. Useful exceptions
can be used for adaptation="segment": Specifically
alpha (default 0.05) defines the significance level for the
signal detection. It can be chosen between 0.01 and 0.2 as for
other values we did not determine the critical values for the
statistical tests. delta (default 0) defines the minimum
signal which should be detected.
restricted determines if smoothing for voxel detected to be significant is restricted to use only voxel from the same segment. The
default is restricted=FALSE. restricted slightly changes
the behaviour under the alternative, i.e. not the interpretation of results.
Joerg Polzehl polzehl@wias-berlin.de, Karsten Tabelow tabelow@wias-berlin.de
This function performs the smoothing on the Statistical Parametric Map spm.
hmax is the (maximal) bandwidth used in the last iteration. Choose
adaptation as "none" for non adaptive
smoothing. lkern can be used for specifying the
localization kernel. For comparison with non adaptive methods use
"Gaussian" (hmax times the voxelsize in x-direction will give the FWHM bandwidth in mm),
for better adaptation use "Plateau" or "Triangle"
(default, hmax given in voxel). For lkern="Plateau" and lkern="Triangle" thresholds may be inaccurate, due to a violation of
the Gaussian random field assumption under homogeneity. lkern="Plateau"
is expected to provide best results with adaptive smoothing.
skern can be used for specifying the
kernel for the statistical penalty. "Plateau" is expected to provide the best results,
due to a less random weighting scheme.
The function handles zero variances by assigning a large value (1e20)
to these variances. Smoothing is restricted to voxel with spm$mask.
Polzehl, J., Voss, H.U., and Tabelow, K. (2010). Structural Adaptive Segmentation for Statistical Parametric Mapping, NeuroImage, 52:515-523.
Tabelow, K., Polzehl, J., Voss, H.U., and Spokoiny, V. (2006). Analysing fMRI experiments with structure adaptive smoothing procedures, NeuroImage, 33:55-62.
Polzehl, J. and Spokoiny, V. (2006). Propagation-Separation Approach for Local Likelihood Estimation, Probab. Theory Relat. Fields 135:335-362.
Polzehl, J. and Tabelow, K. (2007) fmri: A Package for Analyzing fmri Data, R News, 7:13-17 .
if (FALSE) fmri.smooth(spm, hmax = 4, lkern = "Gaussian")
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