In jimeharrisjr/svdtools: SVD Tools for Matrices

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(svdtools)
library(graphics)

Single Value Decomposition can remove noise from matrices in the process of reducing them. One example is image filtering. The included data object noisymatrix is one such example. This is a grayscale image of Linux Penguin on Wikimedia Commons from Larry Ewing [e-mail]. At random, some pixels have been deleted, creating noise.

image(noisymatrix, col=gray.colors(65536))

There are several ways we could filter this image to try to remove the impact of the bad pixels. Let's examine the explanation plots.

#plot_explanation(noisymatrix, limit=.99)

There are a lot of components to play with. One brute force way of doing this would be to try specifying some percentage of components to keep. We could try 98%:

m<-reduce_percentage(noisymatrix, .98)
image(m, col=gray.colors(65536))

This image is obviously overfiltered. Instead, we could simply eliminate all the components above some threshold - for example, discard 51-411:

# Keep the first 50 components
m<-reduce_components(noisymatrix, 50)
image(m, col=gray.colors(65536))

This looks significantly better, but we could try tuning the image to keep more of the data, and removing only a block of components. We can try excluding 51-250:

m<-exclude_components(noisymatrix,51:250)
image(m, col=gray.colors(65536))

In this way, we can gradually select between the level of sharpness and the level of noise we retain!

jimeharrisjr/svdtools documentation built on Jan. 7, 2021, 12:47 a.m.