R/baseline.rollingBall.R

In baseline: Baseline Correction of Spectra

## $Id: baseline.rollingBall.R 170 2011-01-03 20:38:25Z bhm $


#' @title Rolling ball
#' 
#' @description Ideas from Rolling Ball algorithm for X-ray spectra by M.A.Kneen and H.J.
#' Annegarn. Variable window width has been left out
#' 
#' @aliases baseline.rollingBall rollingBall
#' @param spectra Matrix with spectra in rows
#' @param wm Width of local window for minimization/maximization
#' @param ws Width of local window for smoothing
#' @return \item{baseline }{Matrix of baselines corresponding to spectra
#' \code{spectra}} \item{corrected }{Matrix of baseline corrected spectra}
#' @author Kristian Hovde Liland and Bjørn-Helge Mevik
#' @references M.A. Kneen, H.J. Annegarn: Algorithm for fitting XRF, SEM and
#' PIXE X-ray spectra backgrounds
#' @keywords baseline spectra
#' @examples
#' 
#' data(milk)
#' bc.rollingBall <- baseline(milk$spectra[1,, drop=FALSE], wm=200, ws=200,
#' 	method='rollingBall')
#' \dontrun{
#' 	plot(bc.rollingBall)
#' }
#' @export
baseline.rollingBall <- function(spectra, wm, ws){
  ## Ideas from Rolling Ball algorithm for X-ray spectra by M.A.Kneen
  ## and H.J. Annegarn. Variable window width has been left out
  #
  # INPUT:
  # spectra - rows of spectra
  # wm      - width of local window for minimization/maximization
  # ws      - width of local window for smoothing
  #
  # OUTPUT:
  # baseline  - proposed baseline
  # corrected - baseline corrected spectra
  
  np <- dim(spectra)
  
  # Initialization
  y        <- numeric(np[2]) # Spectrum
  T1       <- numeric(np[2]) # Minimizers
  T2       <- numeric(np[2]) # Maximizers
  basel    <- numeric(np[2]) # Smoothers
  baseline <- matrix(0,np[1],np[2]) # Final baseline
  u1       <- 0 # Place holder #1
  u2       <- 0 # Place holder #2
  v        <- 0 # Sum holder
  
  # Loop through spectra
  for(a in 1:np[1]){
    y <- spectra[a,]
    # Minimize
    u1 <- ceiling((wm+1)/2)+1
    T1[1] <- min(y[1:u1])
    for(i in 2:wm){                  # -- Start of spectrum --
      u2 <- u1+1+(i%%2)
      T1[i] <- min(y[(u1+1):(u2)],T1[i-1]) # Check if new is smaller
      u1 <- u2
    }
    for(i in (wm+1):(np[2]-wm)){     # -- Main part of spectrum --
      if((y[u1+1]<=T1[i-1]) && (y[u1-wm]!=T1[i-1]))
        T1[i] <- y[u1+1]   # Next is smaller
      else
        T1[i] <- min(y[(i-wm):(i+wm)])
      u1 <- u1+1
    }
    u1 <- np[2]-2*wm-1
    for(i in (np[2]-wm+1):np[2]){    # -- End of spectrum --
      u2<- u1+1+((i+1)%%2)
      if(min(y[u1:(u2-1)])>T1[i-1])
        T1[i] <- T1[i-1]   # Removed is larger
      else
        T1[i] <- min(y[(u2):np[2]])
      u1 <- u2
    }
    
    # Maximize
    u1 <- ceiling((wm+1)/2)+1
    T2[1] <- max(T1[1:u1])
    for(i in 2:wm){                  # -- Start of spectrum --
      u2 <- u1+1+(i%%2)
      T2[i] <- max(T1[(u1+1):(u2)],T2[i-1]) # Check if new is larger
      u1 <- u2
    }
    for(i in (wm+1):(np[2]-wm)){     # -- Main part of spectrum --
      if((T1[u1+1] >= T2[i-1]) && (T1[u1-wm]!=T2[i-1]))
        T2[i] <- T1[u1+1] # Next is larger
      else
        T2[i] <- max(T1[(i-wm):(i+wm)])
      u1 <- u1+1
    }
    u1 <- np[2]-2*wm-1
    for(i in (np[2]-wm+1):np[2]){    # -- End of spectrum --
      u2<- u1+1+((i+1)%%2)
      if(max(T1[u1:(u2-1)])<T2[i-1])
        T2[i] <- T2[i-1]   # Removed is smaller
      else
        T2[i] <- max(T1[(u2):np[2]])
      u1 <- u2
    }
    
    # Smooth
    u1 <- ceiling(ws/2)
    v <- sum(T2[1:u1])
    for(i in 1:ws){                  # -- Start of spectrum --
      u2<-u1+1+(i%%2)
      v <- v+sum(T2[(u1+1):u2])      # Sum so far
      basel[i] <- v/u2               # Mean so far
      u1 <- u2
    }
    v <- sum(T2[1:(2*ws+1)])
    basel[ws+1] <- v/(2*ws+1)
    for(i in (ws+2):(np[2]-ws)){     # -- Main part of spectrum --
      v <- v - T2[i-ws-1] + T2[i+ws] # Sum so far
      basel[i] <- v/(2*ws+1)         # Mean so far
    }
    u1 <- np[2]-2*ws+1
    v <- v-T2[u1]                    # Sum so far
    basel[np[2]-ws+1] <- v/(2*ws)    # Mean so far
    for(i in (np[2]-ws+2):np[2]){    # -- End of spectrum --
      u2 <- u1+1+(i+1)%%2
      v <- v-sum(T2[(u1):(u2-1)])    # Sum so far
      basel[i] <- v/(np[2]-u2+1)     # Mean so far
      u1 <- u2
    }
    baseline[a,] <- basel
  }
  
  corrected <- spectra-baseline
  list(baseline=baseline, corrected=corrected)
}