The functions perform adaptive weights smoothing for data in orientation space SE(3),
e.g. diffusion weighted MR data,
with spatial coordinates given by voxel location within a mask and spherical information given
by gradient direction. Observations can belong to different shells characterized by b-value bv.
The data provided should only refer to voxel within mask.
smse3ms(sb, s0, bv, grad, kstar, lambda, kappa0, mask, sigma,
ns0 = 1, ws0 = 1, vext = NULL, ncoils = 1, verbose = FALSE, usemaxni = TRUE)
smse3(sb, s0, bv, grad, mask, sigma, kstar, lambda, kappa0,
ns0 = 1, vext = NULL, vred = 4, ncoils = 1, model = 0, dist = 1,
verbose = FALSE)The functions return lists with main results in components
th and th0 containing the smoothed data.
2D array of diffion weighted data, first dimension refers to index ov voxel within the mask, second dimension to the number diffusion weighted images.
vector of length sum(mask) containing values within mask of an average non-diffusion-weigthed image.
vector of b-values.
matrix of gradient directions with dim(grad)[1]==3.
number of steps in adaptive weights smoothing.
Scale parameter in adaptation
determines amount of smoothing on the sphere. Larger values correspond to stronger smoothing
on the sphere. If kappa0=NULL a value is that corresponds to a variace reduction
with factor vred on the sphere.
3D image defining a mask (logical)
Error standard deviation. Assumed to be known and homogeneous in the current implementation.
A reasonable estimate may be defined
as the modal value of standard deviations obtained using method getsdofsb.
Actual number of non-diffusion-weigthed images used to obtain s0 by averaging.
Weight for non-diffusion-weigthed images in statistical penalty.
Voxel extensions.
Effective number of receiver coils (in case of e.g. GRAPPA reconstructions),
should be 1 in case of SENSE reconstructions. 2*ncoils is the number of degrees of freedom of
the intensity distribution used.
If verbose=TRUE additional reports are given.
If "usemaxni==TRUE" a strikter penalization is used.
Used if kappa0=NULL to specify the variance reduction on the
sphere when suggesting a value of kappa0.
Determines which quantities are smoothed. Possible values are
"Chi" for observed values (assumed to be distributed as noncentral
Chi with 2*ncoils degrees of freedom), "Chi2" for squares of
observed values (assumed to be distributed as noncentral
Chi-squared with 2*ncoils degrees of freedom). "Gapprox"
and "Gapprox2" use a Gaussian approximation for the noncentral
Chi distribution to smooth ovserved and squared values, respectively.
Distance in SE3. Reasonable values are 1 (default, see Becker et.al. 2012), 2 ( a slight modification of 1: with k6^2 instead of abs(k6)) and 3 (using a 'naive' distance on the sphere)
J\"org Polzehl polzehl@wias-berlin.de
Joerg Polzehl, Karsten Tabelow (2019). Magnetic Resonance Brain Imaging: Modeling and Data Analysis Using R. Springer, Use R! series. Doi:10.1007/978-3-030-29184-6.
S. Becker, K. Tabelow, H.U. Voss, A. Anwander, R. Heidemann, J. Polzehl. Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS). Medical Image Analysis, 2012, 16, 1142-1155. DOI:10.1016/j.media.2012.05.007.
S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl. Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS. Neuroimage, 2014, 95, 90-105. DOI:10.1016/j.neuroimage.2014.03.053.