awssigmc: Estimate noise variance for multicoil MR systems
In neuroconductor/dti: Analysis of Diffusion Weighted Imaging (DWI) Data

Description Usage Arguments Value Author(s) References

The distribution of image intensity values S_i divided by the noise standard deviation in K-space σ in dMRI experiments is assumed to follow a non-central chi-distribution with 2L degrees of freedom and noncentrality parameter η, where L refers to the number of receiver coils in the system and σ η is the signal of interest. This is an idealization in the sense that each coil is assumed to have the same contribution at each location. For realistic modeling L should be a locally smooth function in voxel space that reflects the varying local influence of the receiver coils in the the reconstruction algorithm used.

The functions assume L to be known and estimate either a local (function awslsigmc) or global ( function awssigmc) σ employing an assumption of local homogeneity for the noncentrality parameter η.

Function afsigmc implements estimates from Aja-Fernandez (2009). Function aflsigmc implements the estimate from Aja-Fernandez (2013).

awssigmc(y, steps, mask = NULL, ncoils = 1, vext = c(1, 1), lambda = 20, 
         h0 = 2, verbose = FALSE, sequence = FALSE, hadj = 1, q = 0.25, 
         qni = .8, method=c("VAR","MAD"))
awslsigmc(y, steps, mask = NULL, ncoils = 1, vext = c(1, 1), lambda = 5, minni = 2, 
         hsig = 5, sigma = NULL, family = c("NCchi"), verbose = FALSE, 
         trace=FALSE, u=NULL)
afsigmc(y, level = NULL, mask = NULL,  ncoils = 1,   vext = c( 1, 1),   
        h = 2, verbose = FALSE, hadj = 1, 
        method = c("modevn","modem1chi","bkm2chi","bkm1chi"))
aflsigmc(y, ncoils, level = NULL, mask = NULL, h=2, hadj=1,  vext = c( 1, 1))

`y`	3D array, usually obtained from an object of class `dwi` as `obj@si[,,,i]` for some `i`, i.e. one 3D image from an dMRI experiment.
`steps`	number of steps in adapive weights smoothing, used to reveal the unerlying mean structure.
`mask`	restrict computations to voxel in mask, if `is.null(mask)` all voxel are used. In function `afsigmc` mask should refer to background for `method %in% c("modem1chi","bkm2chi","bkm1chi")` and to voxel within the head for `method=="modevn"`.
`ncoils`	number of coils, or equivalently number of effective degrees of freedom of non-central chi distribution divided by 2.
`vext`	voxel extentions
`lambda`	scale parameter in adaptive weights smoothing
`h0`	initial bandwidth
`verbose`	if `verbose==TRUE` density plots and quantiles of local estimates of `sigma` are provided.
`trace`	if `trace==TRUE` intermediate results for each step are returned in component tergs for all voxel in mask.
`sequence`	if `sequence=TRUE` a vector of estimates for the noise standard deviation `sigma` for the individual steps is returned instead of the final value only.
`hadj`	adjustment factor for bandwidth (chosen by `bw.nrd`) in mode estimation
`q`	quantile to be used for interquantile-differences.
`qni`	quantile of distribution of actual sum of weights N_i=∑_j w_{ij} in adaptive smoothing. Only voxel i with N_i > q_{qni}(N_.) are used for variance estimation. Should be larger than 0.5.
`method`	in case of function `awssigmc` the method for variance estimation, either "VAR" (variance) or "MAD" (mean absolute deviation). In function `afsigmc` see last column in Table 2 in Aja-Fernandez (2009).
`level`	threshold for background separation. Used if `!is.null(level)` to redefine mask
`h`	bandwidth for local avaeraging
`minni`	Minimum sum of weights for updating values of `sigma`.
`hsig`	Bandwidth of the median filter.
`sigma`	Initial estimate for `sigma`
`family`	One of `"Gauss"` or `"NCchi"` (default) defining the probability distribution to use.
`u`	if `verbose==TRUE` an array of noncentrality paramters for comparisons. Internal use for tests only

a list with components

`sigma`	either a scalar or a vector of estimated noise standard deviations.
`theta`	the estimated mean structure

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

K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015), pp. 76–86.

neuroconductor/dti documentation built on May 20, 2021, 4:28 p.m.