filtn: Smoothing Filters using K-nearest neighbors

In kuwisdelu/matter: Out-of-core statistical computing and signal processing

Smoothing Filters using K-nearest neighbors

Description

Smooth a nonuniformly sampled signal in K-nearest neighbors.

Usage

# Moving average filter
filtn_ma(x, index, k = 5L, metric = "euclidean", p = 2)

# Linear convolution filter
filtn_conv(x, index, weights, metric = "euclidean", p = 2)

# Gaussian filter
filtn_gauss(x, index, k = 5L, sd = median(r) / 2,
    metric = "euclidean", p = 2)

# Bilateral filter
filtn_bi(x, index, k = 5L, sddist = median(r) / 2,
    sdrange = mad(x, na.rm=TRUE), metric = "euclidean", p = 2)

# Bilateral filter with adaptive parameters
filtn_adapt(x, index, k = 5L, spar = 1,
    metric = "euclidean", p = 2)

Arguments

x	A numeric vector.
index	A matrix or list of domain vectors giving the sampling locations of x.
k	The number of K-nearest neighbors to use in the smoothing (including the sample being smoothed). Must be positive.
weights	A vector of weights for the linear convolution kernel, in order from nearest to farthest neighbors. The first weight applies to the sample being smoothed.
sd, sddist	The spatial parameter for kernel-based filters. This controls the strength of smoothing for samples farther from the center of the smoothing window. The default is calculated as half the median smoothing radius (i.e., the distance to the Kth nearest neighbor).
sdrange	The range parameter for kernel-based filters. This controls the strength of the smoothing for samples with signal values very different from the center of the smoothing window.
spar	The strength of the smoothing when calculating the adaptive bilateral filtering parameters. The larger the number, the stronger the smoothing. Must be positive.
metric	Distance metric to use when finding the nearest neighbors. Supported metrics include "euclidean", "maximum", "manhattan", and "minkowski".
p	The power for the Minkowski distance.

Details

These functions must first perform a K-nearest neighbors search on the sample locations (index) before smoothing the signal (x), but they can be applied to nonuniformly sampled signals in an arbitrary number of dimensions. The nearest neighbor search is performed using a kd-tree. It is efficient for low dimensional signals, but performance will degrade in high dimensions. In general, the complexity of these filters is O(k * n log(n)).

Value

A numeric vector the same dimensions as x with the smoothed result.

Author(s)

Kylie A. Bemis

References

J. Joseph and R. Perisamy. “An image driven bilateral filter with adaptive range and spatial parameters for denoising Magnetic Resonance Images.” Computers and Electrical Engineering, vol. 69, pp. 782-795, July 2018.

Examples

set.seed(1)

# signal intensities
x <- rlnorm(100)

# 3D sampling locations
index <- replicate(3, runif(100))

filtn_ma(x, index, k=5)

kuwisdelu/matter documentation built on Sept. 18, 2024, 6:31 p.m.