Scale Space Multiresolution Analysis of Random Signals

A method for the multiresolution analysis of spatial fields and images to capture scale-dependent features. mrbsizeR is based on scale space smoothing and uses differences of smooths at neighbouring scales for finding features on different scales. To infer which of the captured features are credible, Bayesian analysis is used. The scale space multiresolution analysis has three steps: (1) Bayesian signal reconstruction. (2) Using differences of smooths, scale-dependent features of the reconstructed signal can be found. (3) Posterior credibility analysis of the differences of smooths created. The method has first been proposed by Holmstrom, Pasanen, Furrer, Sain (2011) and extended in Flury, Gerber, Schmid and Furrer (2021) .

mrbsizeR

Installation

The preferred way to install mrbsizeR from CRAN is:

install.packages("mrbsizeR")

You can install the mrbsizeR devel version from github with:

# install.packages("devtools")
devtools::install_github("romanflury/mrbsizeR")

Example

# Artificial sample data
set.seed(987)
sampleData <- matrix(stats::rnorm(100), nrow = 10)
sampleData[4:6, 6:8] <- sampleData[4:6, 6:8] + 5

# Generate samples from multivariate t-distribution
tSamp <- rmvtDCT(object = sampleData, lambda = 0.2, sigma = 6, nu0 = 15,
                  ns = 1000)
 
# mrbsizeRgrid analysis
mrbOut <- mrbsizeRgrid(posteriorFile = tSamp$sample, mm = 10, nn = 10,
                       lambdaSmoother = c(1, 1000), prob = 0.95)

# Posterior mean of the differences of smooths
plot(x = mrbOut$smMean, turn_out = TRUE)

# Credibility analysis using simultaneous credible intervals
plot(x = mrbOut$ciout, turn_out = TRUE)