JPLLK_surface {DRIP} R Documentation

## Denoising and jump-preserving

### Description

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

### 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.

### Value

A list of fitted values, residuals, chosen bandwidth and estimated sigma.

### References

Qiu, P., "Jump-preserving surface reconstruction from noisy data", Annals of the Institute of Statistical Mathematics, 61(3), 2009, 715-751.

threeStage, surfaceCluster
data(sar) # SAR image is bundled with the package and it is a