Smoothing Statistical Parametric Maps

Perform the adaptive weights smoothing procedure

fmri.smooth(spm, hmax = 4, adaptation="aws",
            lkern="Gaussian", skern="Plateau", weighted=TRUE,...)

Arguments

spm	object of class `fmrispm`
hmax	maximum bandwidth to smooth
adaptation	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	`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	`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	`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. Usefull exceptions can be used for `adaptation="segment"`: Specifically `alpha` (default 0.05) defines the significance level for the signal detection. It can be choosen 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` slighty changes the behaviour under the altenative, i.e. not the interpretation of results.

Details

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.

Value

object with class attributes "fmrispm" and "fmridata", or "fmrisegment" and "fmridata" for segmentation choice

cbeta

smoothed parameter estimate

var

variance of the parameter

hmax

maximum bandwidth used

rxyz

smoothness in resel space. all directions

rxyz0

smoothness in resel space as would be achieved by a Gaussian filter with the same bandwidth. all directions

scorr

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.

dim

dimension of the data cube and residuals

weights

ratio of voxel dimensions

vwghts

ratio of estimated variances for the stimuli given by vvector

hrf

Expected BOLD response for the specified effect

References

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 .

Author

Joerg Polzehl polzehl@wias-berlin.de, Karsten Tabelow tabelow@wias-berlin.de

Examples

if (FALSE) fmri.smooth(spm, hmax = 4, lkern = "Gaussian")