Short introduction

Noise in diffusion-weighted MRI data is an artifact related to the randomess in the data from various sources, e.g., the thermal or physiological noise. msPOAS (multi-shell Position-Orientation Adaptive Smoothing) is a method to adaptively denoise diffusion-weighted MRI data, acquired on one or shell shells. It has been outlined for single-shell dMRI data in Becker et al. (2012) and refined for multi-shell dMRI data in Becker et al. (2014) (which can be used for single-shell data, too). There exist two implementations of msPOAS, one in the R software environment for statistical computing and graphics as package dti and as part of the ACID toolbox for SPM. The latter has been described in detail in Tabelow et al. (2015).

Use msPOAS

The msPOAS toolbox has a number of input choices to make, as described below. DTI images, Diffusion directions, and b-values correspond to the data. Preferrably correction for susceptibility artifacts and addy-current and motion correction should be already performed. k star, kappa, and lambda are parameters of msPOAS. Furthermore it is important to give a suitable estimate for the noise standard deviation sigma. This can, e.g., be obtained using the background estimator coming with this toolbox. Mis-specifications of sigma will leads to oversmoothing or little noise reduction. The effective number of recveiver coils ncoils is difficult to estimate. You can leave it as 1 even for parallel acquisitions as long as the noise estimation uses the same value.

Specifically the choices for the msPOAS tollbox are:

• DTI images: Select the N high and low b-value images of the dataset. The order of the files in not important as long as diffusion directions and b-values are given in the same order.

• Diffusion directions: Provide an 3xN matrix of b-vectors in the same order as the low-and high b-value images above were entered. Evaluated statements can be used.

• b-values: Provide a vector of N b-values in the same order as the low-and high b-value images above were entered. Note, that the data must be acquired using one or more spherical shells. msPOAS is not suitable for DSI data. Evaluated statements can be used.

• k star: msPOAS is an iterative procedure, low numbers of iterations reduce data variance little, while large numbers of iterations increase smoothness of the result as well as the computing time. Although, msPOAS includes an automatic stopping rule, a misspecification of the noise level (see below) may lead to over-smoothing or little noise reduction only. If you are unsure, use 10 or 12 as default, for a good smoothing performance while still being not too exhaustive.

Fig. 1: Example(!) of the dependence of the computation time of msPOAS on the number of iteration steps. The example is taken from Tabelow et al. (2015).

Fig. 2: Dependence of the FA in a DTI model evaluation of the same example data on the number of iteration steps. Reproduction of Figure 6 of Tabelow et al. (2015).

• kappa: msPOAS relates the amount of smoothing on the orientation (shell) space with the position (voxel) space. kappa is the numeric parameter for this. If you are unsure use the default 0.8.!

Fig. 3: Choice of kappa depending on the mean number of acquired gradients per shell. Inspired by Figure 2 of Tabelow et al. (2015).

Fig. 4: Dependence of the estimated FA in a DTI model evaluation of the example data in Tabelow et al. (2015) on kappa. Reproduction of Figure 8 of Tabelow et al. (2015).

• lambda: This is the adaptation bandwidth of the procedure, the default is 10 and is determined by simulation. If the noise level is determined correctly (see below), there should be no need to change this! If you change it nonetheless, larger values of lambda (up to infinity) reduce adaptivity of the procedure, smaller values lead to less noise reduction.

Fig. 5: Dependence of the estimated FA in a DTI model evaluation of the example data in Tabelow et al. (2015) on the adaptation parameter lambda. Larger values of lambda lead to less adaptivity of msPOAS and hence to blurring of a non-adaptive smoother. Reproduction of Figure 7 of Tabelow et al. (2015).

• sigma: This parameter must be determined from a third party tool (cf. the estimation tool in this toolbox). Over-estimation of sigma leads to blurring, while under-estimation leads to a reduced smoothing effect. This corresponds to changes in the choice of lambda, see there. Later versions of this toolbox will automatically determine the (local) noise level.

• ncoils: This is the number of effective receiver coils for the acquisition. It should be the same as for the determination of sigma (which also depends on ncoils). If unsure, choose 1 for both as approximation!

References

Saskia Becker, Karsten Tabelow, Henning U. Voss, Alfred Anwander, Robin M. Heidemann, and Jörg Polzehl (2012). Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS). Medical Image Analysis, 16(6): 1142--1155, DOI: 10.1016/j.media.2012.05.007.

(Please cite this paper when referring to the original single shell POAS method)

Saskia Becker, Karsten Tabelow, Siawoosh Mohammadi, Nikolaus Weiskopf, and Jörg Polzehl (2014). Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS. NeuroImage, 95: 90-105, DOI: 10.1016/j.neuroimage.2014.03.053.

(Please cite this paper when referring to the msPOAS method)

Karsten Tabelow, Siawoosh Mohammadi, Nikolaus Weiskopf, and Jörg Polzehl (2015). POAS4SPM - a toolbox for SPM to denoise diffusion MRI data. NeuroInformatics, 13: 19-29, DOI:10.1007/s12021-014-9228-3.

(Please cite this paper when using this toolbox)