Monday, 15 October 2012

Compressed Sensing with R

Compressed sensing (CS) is pretty much appealing all current signal processing research community. At the same time, popularity of R language gaining a strong foot in the research and industry. Even though historically MATLAB is a de-facto standard in signal processing community, R is becoming a serious alternative to this. For example, the quality of R in time-series analysis or medical imaging is now an accepted fact. 

Last year, I have demonstrated how one can use R in compressed sensing research in a
short tutorial in the pub, close to Liverpool street in London.  The package R1magic is available in CRAN. Package provides basic interface to perform 1-D compressed sensing with l1, TV penalized minimization. There are other packages doing similar regularized minimization. However the interface of R1magic is particularly designed for CS i.e. appearance of sparse bases in the objective function.  

Here is one simple example (
Version 0.1):

library(R1magic)#  Signal components
N <- 100
# Sparse components

K <- 4 
#  Up to Measurements  > K LOG (N/K)
M <- 40
# Measurement Matrix (Random Sampling Sampling)
phi <- GaussianMatrix(N,M)
# R1magic generate random signal
xorg <- sparseSignal(N, K, nlev=1e-3)
y <- phi %*% xorg ;# generate measurement
T <- diag(N) ;# Do identity transform
p <- matrix(0, N, 1) ;# initial guess
# R1magic Convex Minimization ! (unoptimized-parameter)
ll <- solveL1(phi, y, T, p)
x1 <- ll$estimate
plot( 1:100, seq(0.011,1.1,0.011), type = "n",xlab="",ylab="")
title(main="Random Sparse Signal Recovery",
      xlab="Signal Component",ylab="Spike Value")
lines(1:100, xorg , col = "red")
lines(1:100, x1, col = "blue", cex = 1.5) 

# shifted by 5 for clearity

Blue line is the reconstructed signal with R1magic.

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(c) Copyright 2008-2015 Mehmet Suzen (suzen at acm dot org)

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