R: Adaptive smoothing in orientation space SE(3)

smse3ms {aws} | R Documentation

## 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, 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.
`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 polzehl@wias-berlin.de

### 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.

[Package aws version 2.4-0 Index]