smse3ms {aws}

Adaptive smoothing in orientation space SE(3)

Description

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.

Usage

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 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.

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.

Note

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

Author(s)

J\"org Polzehl [e-mail]

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.