vpaws {aws}  R Documentation 
vector valued version of function paws
with homogeneous covariance structure
Description
The function implements a vectorvalued version the propagation separation approach that
uses patches instead of individuel voxels for comparisons in parameter space. Functionality is analog to function vaws
. Using patches allows for an improved
handling of locally smooth functions and in 2D and 3D for improved smoothness of
discontinuities at the expense of increased computing time.
Usage
vpaws(y, kstar = 16, sigma2 = 1, invcov = NULL, mask = NULL, scorr = 0, spmin = 0.25,
ladjust = 1, wghts = NULL, u = NULL, patchsize = 1)
vpawscov(y, kstar = 16, invcov = NULL, mask = NULL, scorr = 0, spmin = 0.25, ladjust = 1,
wghts = NULL, maxni = FALSE, patchsize = 1)
vpawscov2(y, kstar = 16, invcov = NULL, mask = NULL, scorr = 0, spmin = 0.25,
lambda = NULL, ladjust = 1, wghts = NULL, patchsize = 1,
data = NULL, verbose = TRUE)
Arguments
y 

kstar 
maximal number of steps to employ. Determines maximal bandwidth. 
sigma2 
specifies a homogeneous error variance. 
invcov 
array (or matrix) of voxelwise inverse covariance matrixes, first index corresponds to upper diagonal inverse covariance matrix. 
mask 
logical mask. All computations are restrikted to design poins within the mask. 
scorr 
The vector 
spmin 
determines the form (size of the plateau) in the adaptation kernel. Not to be changed by the user. 
ladjust 
factor to increase the default value of lambda 
wghts 

u 
a "true" value of the regression function, may be provided to
report risks at each iteration. This can be used to test the propagation condition with 
patchsize 
positive integer defining the size of patches. Number of grid points within the patch is 
maxni 
require growing sum of weights 
lambda 
explicit value of lambda 
data 
optional vectorvalued images to be smoothed using the weighting scheme of the last step 
verbose 
logical: provide information on progress. 
Details
see vaws
.
Parameter y
The procedure is supposed to produce superior results if the assumption of a
local constant image is violated or if smooothness of discontinuities is desired.
Function vpawscov2
is intended for internal use in package qMRI
only.
Value
function vpaws
returns
returns an object of class aws
with slots
y = "numeric" 
y 
dy = "numeric" 
dim(y) 
x = "numeric" 
numeric(0) 
ni = "integer" 
integer(0) 
mask = "logical" 
logical(0) 
theta = "numeric" 
Estimates of regression function, 
hseq = "numeric" 
sequence of bandwidths employed 
mae = "numeric" 
Mean absolute error for each iteration step if u was specified, numeric(0) else 
psnr = "numeric" 
Peak signaltonoise ratio for each iteration step if u was specified, numeric(0) else 
var = "numeric" 
approx. variance of the estimates of the regression function. Please note that this does not reflect variability due to randomness of weights.Currently also uses factor 
xmin = "numeric" 
numeric(0) 
xmax = "numeric" 
numeric(0) 
wghts = "numeric" 
numeric(0), ratio of distances 
degree = "integer" 
0 
hmax = "numeric" 
effective hmax 
sigma2 = "numeric" 
provided or estimated error variance 
scorr = "numeric" 
scorr 
family = "character" 
family 
shape = "numeric" 
shape 
lkern = "integer" 
integer code for lkern, 1="Plateau", 2="Triangle", 3="Quadratic", 4="Cubic", 5="Gaussian" 
lambda = "numeric" 
effective value of lambda 
ladjust = "numeric" 
effective value of ladjust 
aws = "logical" 
aws 
memory = "logical" 
memory 
homogen = "logical" 
homogen 
earlystop = "logical" 
FALSE 
varmodel = "character" 
"Constant" 
vcoef = "numeric" 
numeric(0) 
call = "function" 
the arguments of the call to 
If y
contained only information (condensed data) for positions within a mask, then the returned object only contains
results for these positions.
Note
use setCores='number of threads'
to enable parallel execution.
Author(s)
Joerg Polzehl, polzehl@wiasberlin.de, https://www.wiasberlin.de/people/polzehl/
References
J. Polzehl, K. Tabelow (2019). Magnetic Resonance Brain Imaging: Modeling and Data Analysis Using R. Springer, Use R! series. Appendix A. Doi:10.1007/9783030291846.
J. Polzehl, K. Papafitsoros, K. Tabelow (2020). PatchWise Adaptive Weights Smoothing in R, Journal of Statistical Software, 95(6), 127. doi:10.18637/jss.v095.i06 .
See Also
See also vaws
, lpaws
, vawscov
,link{awsdata}
Examples
## Not run:
setCores(2)
y < array(rnorm(4*64^3),c(4,64,64,64))
yhat < vpaws(y,kstar=20)
## End(Not run)