3D variance estimation — awsLocalSigma • aws

Functions for 3D variance estimation. awsLocalSigma implements the local adaptive variance estimation procedure introduced in Tabelow, Voss and Polzehl (2015). awslinsd uses a parametric model for varianc/mesn dependence. Functions AFLocalSigma and estGlobalSigma implement various proposals for local and global variance estimates from Aja-Fernandez (2009, 2013) and a global variant of the approach from Tabelow, Voss and Polzehl (2015).

awsLocalSigma(y, steps, mask, ncoils, vext = c(1, 1), lambda = 5,
    minni = 2, hsig = 5, sigma = NULL, family = c("NCchi", "Gauss"),
    verbose = FALSE, trace = FALSE, u = NULL)
awslinsd(y, hmax = NULL, hpre = NULL, h0 = NULL, mask = NULL,
    ladjust = 1, wghts = NULL, varprop = 0.1, A0, A1)
AFLocalSigma(y, ncoils, level = NULL, mask = NULL, h = 2, hadj = 1,
    vext = c(1, 1))
estGlobalSigma(y, mask = NULL, ncoils = 1, steps = 16, vext = c(1, 1),
    lambda = 20, hinit = 2, hadj = 1, q = 0.25, level = NULL,
    sequence = FALSE, method = c("awsVar", "awsMAD", "AFmodevn",
                "AFmodem1chi", "AFbkm2chi", "AFbkm1chi"))
estimateSigmaCompl(magnitude, phase, mask, kstar = 20, kmin = 8, hsig = 5,
        lambda = 12, verbose = TRUE)

Arguments

y	3D array of image intensities.
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 `estGlobalSigma` mask should refer to background for `method %in% c("modem1chi","bkm2chi","bkm1chi")` and to voxel within the head for `method=="modevn"`.
ncoils	effective number of coils, or equivalently number of effective degrees of freedom of non-central chi distribution divided by 2.
vext	voxel extentions or relative voxel extensions
lambda	scale parameter in adaptive weights smoothing
minni	minimal bandwidth for calculating local variance estimates
hsig	bandwwidth for median filter
sigma	optional initial global variance estimate
family	type of distribution, either noncentral Chi ("NCchi") or Gaussian ("Gauss")
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.
u	if `verbose==TRUE` an array of noncentrality paramters for comparisons. Internal use for tests only
hmax	maximal bandwidth
hpre	minimal bandwidth
h0	bandwidth vector characterizing to spatial correlation as correlation induced by convolution with a Gaussian kernel
ladjust	correction factor for lambda
wghts	relative voxel extensions
varprop	defines a lower bound for the estimated variance as `varprop*mean(sigma2hat`
A0	select voxel with `A0 < theta < A1` to estimate parameters of the variance model
A1	select voxel with `A0 < theta < A1` to estimate parameters of the variance model
level	threshold for mask definition
h	bandwidth for local variance estimates.
hinit	minimal bandwidth for local variance estimates with `method="awsxxx"`.
hadj	bandwidth for mode estimation
q	Quantile for interquantile estimate of standard deviation
sequence	logical, return sequence of estimated variances for iterative methods.
method	determines variance estimation method
magnitude	magnitude of complex 3D image
phase	phase of complex 3D image
kstar	number of steps in adapive weights smoothing, used to reveal the unerlying mean structure.
kmin	iteration to start adaptation

Value

all functions return lists with variance estimates in component sigma

References

K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015), 76--86. DOI:10.1016/j.media.2014.10.008.

S. Aja-Fernandez, V. Brion, A. Tristan-Vega, Effective noise estimation and filtering from correlated multiple-coil MR data. Magn Reson Imaging, 31 (2013), 272-285. DOI:10.1016/j.mri.2012.07.006

S. Aja-Fernandez, A. Tristan-Vega, C. Alberola-Lopez, Noise estimation in single- and multiple-coil magnetic resonance data based on statistical models. Magn Reson Imaging, 27 (2009), 1397-1409. DOI:10.1016/j.mri.2009.05.025.

Author

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