Estimate surface using piecewise local linear
kernel smoothing. Bandwidth is chosen by leave-one-out cross validation.
Usage
JPLLK_surface(image, bandwidth, plot = FALSE)
Arguments
image
A square matrix object of size n by n, no missing
value allowed.
bandwidth
A numeric vector with positive integers, which
specify the number of pixels used in the local smoothing. The
final fitted surface chooses the optimal bandwidth from those
provided by users.
plot
If plot = TRUE, the image of the fitted surface is
plotted
Value
A list of fitted values, residuals, chosen bandwidth and
estimated sigma.
Details
At each pixel, the gradient is estimated by a local linear
kernel smoothing procedure. Next, the local neighborhood is
divided into two halves along the direction perpendicular to
(\(\widehat{f}'_{x}\), \(\widehat{f}'_{y}\)). Then the one-
sided local linear kernel (LLK) estimates are obtained in the
two half neighborhoods respectively. Among these two one-sided
estimates, the one with smaller weighted mean square error is
chosen to be the final estimate of the regression surface at the
pixel.
References
Qiu, P., "Jump-preserving surface reconstruction from noisy data", Annals
of the Institute of Statistical Mathematics, 61(3), 2009, 715-751.
# NOT RUN {data(sar) # SAR image is bundled with the package and it is a # standard test image in statistics literature.fit = JPLLK_surface(image=sar, bandwidth=c(3, 4))
# }