Adaptive smoothing in orientation space SE(3)

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)

Arguments

sb	2D array of diffion weighted data, first dimension refers to index ov voxel within the mask, second dimension to the number diffusion weighted images.
s0	vector of length `sum(mask)` containing values within mask of an average non-diffusion-weigthed image.
bv	vector of b-values.
grad	matrix of gradient directions with `dim(grad)[1]==3`.
kstar	number of steps in adaptive weights smoothing.
lambda	Scale parameter in adaptation
kappa0	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.
mask	3D image defining a mask (logical)
sigma	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`.
ns0	Actual number of non-diffusion-weigthed images used to obtain `s0` by averaging.
ws0	Weight for non-diffusion-weigthed images in statistical penalty.
vext	Voxel extensions.
ncoils	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.
verbose	If `verbose=TRUE` additional reports are given.
usemaxni	If `"usemaxni==TRUE"` a strikter penalization is used.
vred	Used if `kappa0=NULL` to specify the variance reduction on the sphere when suggesting a value of `kappa0`.
model	Determines which quantities are smoothed. Possible values are `"Chi"` for observed values (assumed to be distributed as noncentral Chi with `2ncoils` degrees of freedom), `"Chi2"` for squares of observed values (assumed to be distributed as noncentral Chi-squared with `2ncoils` degrees of freedom). `"Gapprox"` and `"Gapprox2"` use a Gaussian approximation for the noncentral Chi distribution to smooth ovserved and squared values, respectively.
dist	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)

Value

The functions return lists with main results in components th and th0 containing the smoothed data.

References

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.

Author

J\"org Polzehl polzehl@wias-berlin.de

Note

These functions are intended to be used internally in package dti only.