awsLocalSigma {aws}

3D variance estimation

Description

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).

Usage

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

Author(s)

J\"org Polzehl [e-mail]

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.