R: 3D variance estimation

awsLocalSigma {aws} | R Documentation

## 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 polzehl@wias-berlin.de

### 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.

[Package aws version 2.5-1 Index]