paws {aws}  R Documentation 
Adaptive weigths smoothing using patches
Description
The function implements a version the propagation separation approach that
uses patches instead of individuel voxels for comparisons in parameter space. Functionality is analog to function aws
. 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
paws(y, hmax = NULL, mask=NULL, onestep = FALSE, aws = TRUE, family = "Gaussian",
lkern = "Triangle", aggkern = "Uniform", sigma2 = NULL, shape = NULL,
scorr = 0, spmin = 0.25, ladjust = 1, wghts = NULL, u = NULL,
graph = FALSE, demo = FALSE, patchsize = 1)
Arguments
y 
array 
mask 
logical array defining a mask. All computations are restricted to the mask. 
hmax 

onestep 
apply the last step only (use for test purposes only) 
aws 
logical: if TRUE structural adaptation (AWS) is used. 
family 

lkern 
character: location kernel, either "Triangle", "Plateau", "Quadratic", "Cubic" or "Gaussian". The default "Triangle" is equivalent to using an Epanechnikov kernel, "Quadratic" and "Cubic" refer to a Biweight and Triweight kernel, see Fan and Gijbels (1996). "Gaussian" is a truncated (compact support) Gaussian kernel. This is included for comparisons only and should be avoided due to its large computational costs. 
aggkern 
character: kernel used in stagewise aggregation, either "Triangle" or "Uniform" 
sigma2 

shape 
Allows to specify an additional shape parameter for certain family models. Currently only used for family="Variance", that is 
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 
graph 
If 
demo 
If 
patchsize 
positive integer defining the size of patches. Number of grid points within the patch is 
Details
see aws. 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.
Value
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. 
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 
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 aws
, lpaws
, vpaws
,link{awsdata}
Examples
## Not run:
setCores(2)
y < array(rnorm(64^3),c(64,64,64))
yhat < paws(y,hmax=6)
## End(Not run)