# denoise1: Total Variation Denoising for Signal In tvR: Total Variation Regularization

## Description

Given a 1-dimensional signal f, it solves an optimization of the form,

u^* = argmin_u E(u,f)+λ V(u)

where E(u,f) is fidelity term and V(u) is total variation regularization term. The naming convention of a parameter method is <problem type> + <name of algorithm>. For more details, see the section below.

## Usage

 1 denoise1(signal, lambda = 1, niter = 100, method = c("TVL2.IC", "TVL2.MM")) 

## Arguments

 signal vector of noisy signal. lambda regularization parameter (positive real number). niter total number of iterations. method indicating problem and algorithm combination.

## Value

a vector of same length as input signal.

## Algorithms for TV-L2 problem

The cost function for TV-L2 problem is

min_u \frac{1}{2} |u-f|_2^2 + λ |\nabla u|

where for a given 1-dimensional vector, |\nabla u| = ∑ |u_{i+1}-u_{i}|. Algorithms (in conjunction with model type) for this problems are

"TVL2.IC"

Iterative Clipping algorithm.

"TVL2.MM"

Majorization-Minorization algorithm.

The codes are translated from MATLAB scripts by Ivan Selesnick.

## References

\insertRef

rudin_nonlinear_1992tvR

\insertRef

selesnick_convex_2015tvR

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ## generate a stepped signal x = rep(sample(1:5,10,replace=TRUE), each=50) ## add some additive white noise xnoised = x + rnorm(length(x), sd=0.25) ## apply denoising process xproc1 = denoise1(xnoised, method = "TVL2.IC") xproc2 = denoise1(xnoised, method = "TVL2.MM") ## plot noisy and denoised signals plot(xnoised, pch=19, cex=0.1, main="Noisy signal") lines(xproc1, col="blue", lwd=2) lines(xproc2, col="red", lwd=2) legend("bottomleft",legend=c("Noisy","TVL2.IC","TVL2.MM"), col=c("black","blue","red"),#' lty = c("solid", "solid", "solid"), lwd = c(0, 2, 2), pch = c(19, NA, NA), pt.cex = c(1, NA, NA), inset = 0.05) 

tvR documentation built on Aug. 23, 2021, 1:08 a.m.